Start at #1. 

Working in pairs, which boats are overlapped?  Which boats owe mark-room to which boats?

At #2, are there new overlaps and new mark-room obligations?  If so, what are they?

Then realize that mark-room includes room and room includes “…space [for the boat entitled to room] to comply with her obligations under the rules of Part 2 and rule 31, while manoeuvring promptly in a seamanlike way.” .. and that Rule 18 is in Part 2. 

The key to this situation is to be found in the definition of Room, which is called up by the definition of Mark-Room. 

Orange is entitled to room to sail to the mark, while complying with her obligations to Green under the rules of Part 2.

So, since you say that Green is entitled to mark room on Orange, Yellow will have to give her the room to comply with that obligation.

Orange has the rights on Yellow for Mark room. Green obtains the rights on Orange, so the ladder goes as follows: Orange will have to give room for Green and therefore also has to call on Yellow for additional room to leave Green room. This is not about Green having no rights on Yellow - it is all about Green having rights on Orange, and Orange having rights on Yellow.  That is my humble opinion.
What I would have done being Orange is head-up lightly to clear overlap with green, and hence only maintaining the rights on yellow - It would make me the winner of this one :-)

Following Angelo's logic, I note that at point 1 Green owes mark-room to Yellow, who owes mark-room to Orange. Then at point 2, Orange begins owing mark-room to Green. It becomes a bizarre cyclical mark-room situation. FIFO logic would have me invoke 18.2f in order to get Yellow and Green around the buoy, but on-water, that's not going to be very successful without a tremendous understanding and communication from the boats. I feel like Vizzini in Princess Bride.

Assuming that the mark is to be left to port.

Going by the diagram
@1

@2

So the next thing that is going to happen is that @3, boats are going to all be overlapped abeam of the mark, and there will be shouting.  Presumably this will include the word 'protest' so there can be a protest hearing.

BUT

The mark-room G us required to give Y initially is 'room to sail to the mark'. I think we need to parse this a little bit so it becomes 'G must not sail so as to compel Y to do other than to sail to the mark', or possibly 'G mustn't get between Y and the mark so as to prevent Y sailing to the mark'.

Note that, reluctantly, I've introduced notions of compulsion or prevention here, that have no corresponding words in the rules or definitions, but I think that it's the only way to move this forward.

Y is going to say:  G was required to give me room to sail to the mark:  there she was pushing O towards me, and herself sitting between me that the mark:  G did not give me mark-room and broke rule 18.2(b).

G might respond:  No.  Y was responding to R, keeping clear of her and giving her mark-room, and I just sailed into the space made available by O, as  I was entitled to do in accordance with case 63.

Y might come back with:  No, G pushed O outside the mark-room she would have been entitled to in the absence of G, and in that way compelled me to sail wide of the mark.

And the protest committee would have to find some more facts and proceed to a decision.

HOWEVER

In practice, I think it might come out a bit simpler than that.

Diagrams are all very well to develop hypothetical scenarios, but a diagram can convey an inappropriate level of precision, that can't be proved by real world evidence.

OP diagram shows two positions, about 1.5 boat lengths apart.  With boats doing 4 or 5 kts, that's about 3 seconds apart.

I think that in a protest hearing, it's going to be very hard to get evidence about exactly when boats reached the zone and when overlaps were obtained or broken.

That's what rule 18.2(e) (and the concept of last point of certainty) is for.

I think that in a protest hearing, the protest committee would probably be satisfied that there was a last point of certainty a little before G reached the zone where Y and O were overlapped, and G was CASTN of both of them.

Overlap between Y and O doesn't meaningfully change, so G is required to give mark-room to O, no problems.

G was initially CASTN, so there is doubt that she obtained her overlap in time, so it shall be presumed that she did not (rule 18.2(e)).

So it becomes a simple late inside overlap:  G is required to give mark-room to both O and Y, and she interferes with their mark-rounding at her peril.

Yellow would have to give room to green as long as at the point that green gained that room, yellow was still able to give room which on this diag he could

Being something of an expert at muddling myself by overthinking, I think I recognise the symptoms.
I don't think I know of any cases where a boat is required to consider its rule position versus craft several boats away. Please correct me if I'm wrong. Isn't it always pairs of adjacent boats that are considered in the case book?

Consider: if we expand this hypothetical situation to 4 or 5 boats then it starts getting ludicrous, and one may easily get to the situation where an inside overlapped boat is forced the wrong side of the mark, and no clarity is possible. I have a rule of thumb that if I start thinking myself into effectively unmanageable situations then most likely I have overthought myself into error.
I submit the only time the relationship between green and yellow would be relevant would be if orange contrived to capsize in the zone or otherwise cease rounding the mark.

There are some fundamental concepts that I think people are not applying properly or describing in a way that just causes confusion.

First is the notion of 'rights' instead of using the notion of 'entitlement'.  Boats are entitled or not to mark-room based on on Rule 18.  There are no 'rights' there.  If you use the words interchangeably it causes confusion.  The right of way does not change just because you are entitled to mark-room.

Second, as Angelo pointed out, you have to apply the rules to the individual pairs of boats; (1) Orange v Yellow, (2) Orange v Green, (3) Yellow v Green in each position.

So applying the rules to each position:

Position 1:
Pair 1 - O v Y

Pair 2 - O v G

Pair 3 - Y v G

Position 2:
Pair 1 - O v Y

Pair 2 - O v G

Pair 3 - Y v G

When all is said and done and all the obligations are merged together, based on Position 2, 

As things progress to position 3 (not shown) and G gybes to stbd and becomes an inside ROW boat, provided the overlap remains, she will be limited by 18.4.  If G does not maintain the overlap then 18.4 would not apply.  In either case, O's proper course w.r.t. Y will be to give G mark-room.

I think the key point that John Christman has included (and may have been missed by John Allan) is that the mark-room that O is entitled to from Y includes room for O to fulfill her obligations under Part 2 rules, namely rule 18.2(b).
At the moment O enters the zone with G overlapped, O is required to give G mark-room.  O will need room from Y in order to fulfill her obligation to G.
In a protest hearing, it may well be that O could contest that G established an overlap in time, creating a reasonable doubt.  However, going by the OP's description, we can assume that O has acknowledged that G established the overlap in time, there is no doubt, and 18.2(e) does not apply.

@John Christman - you are right - at the end Green has ROW to Orange where Yellow has to give ROW to Orange who has to give Green enough room. This is how I see it as a experienced tactician and how I would instruct my skipper. But if I was on Orange I would have cleared my stern to Green before the zone, called them they have no room and would claim my room to Yellow. Leaving Green and Yellow to sort out their own thing....  

BUT - what I see most in this post is very theoretical breakdown of how rules apply step by step 18, 10 etc per event. To me that is typical Jury talk and approach. The main reason I prefer to stay out of protest hearings Since as a sailor this whole situation has to be called within a minute, max 2 .... and folks do often lie once they are in a hearing so then the whole thing often goes sideways ....18.2 (e) is the scape goat here.....

@Gijs
In a hearing, I have as much problem with 'clearing my stern' just before or right at the zone as I do with late overlaps being established.  When I am advising people about the rules, I tell them that they should be having a dialog with the other boat well before reaching the zone, i.e. at 10 boat lengths or more.  Get an agreement from the other boat as you are sailing on the leg as to whether an overlap exists or not.  If you think the relationship has changed, say so and get agreement, if possible.  As a juror, I am more than happy to rely on 18.2(e) to go back to the last point of certainty when both boats agreed to the relationship.  If at all possible, I avoid trying to figure out what the relationship actually was at the zone.  It is impossible to do accurately and just wastes a huge amount of time.

@John Christman
That is (out of experience ) exactly what I do - communicate with other ship(s) ahead of when a potential situation will occur. Eye-contact, signalling with hands and a call way upfront. In cases of overlap always physically on the stern or bow. A dialogue is always preferred and as a rule of thumb I prefer avoiding any protest but will stick an elbow out when it matters for critical standing/points. Choosing the wrong duels/battles often turns out into a bigger loss than avoiding a cluster-mess and remain sailing free on your own plan. When I "foul up" (everyone does one day...) or it may be dubious I will make a humble gesture including that I will give one back, and after a race I will immediately go for a beer and talk. This way most competitors recognize me as a fair sailor, not a rule-terrorist ...  It is like Paul Elvstrom: You have not won unless you have the respect of your fellow competitors.