SIs will state the course to be sailed, or courses possible to be sailed, and method for signalling which of the courses described in the SIs is to be sailed for the upcoming race.

Sometimes that is true, but in most of our races the SI's  only list the marks that can be used.  This is a 7 race series and every week the course is different.  The course to be used for the current race is posted on a board on the RC boat and announced on VHF shortly before the race.  The issue is whether there are any restrictions on changing the course before the first warning once a course has been posted.

If your Sis don't make the process clear on how the course will be displayed and clearly define the whole process for signalling the when and how of signalling possible changes I think it is time to do some work on your SIs. To me, if the SIs in your situation do not outline a process to change the course after it is posted on the board and announced on the VHF, then the course cannot be changed. 

The RYA have a case that I think covers this, case RYA2008/2. 
In the decision they state:
When Danger Mouse arrived in the start area she observed a valid course being displayed and was, therefore, under no obligation to look further.

While this case is about simultaneous display of courses I think it would apply in the case of changing a course. 

I also appealed a race where the course was changed a short time before the warning signal which was upheld but there were some specific NoR and SI that were also relevant. 

If a course change needs to happen after it is displayed, I would think it best to Postpone and display flag L so that boats should “come within hail” and be told of the change. 

Within the rule itself there is no requirement for the RC to "notify" competitors if they change their mind and signal a new course prior to the warning; the valid course is the one displayed immediately prior to the warning signal.  In other words at 5 minutes before the warning the course is posted as "A" and at 30 seconds before the warning the RC decides that course "A" won't work and decide to change to course "B". They can do that within the rule.  Is it smart? No.  Is it good customer service? No. Is it likely to confuse the competitors? Most likely! So even though they CAN do it without breaking a rule and your likelihood of getting redress may be low (or should be since you don't satisfy the "through no fault of your own"), it is really poor race management.  Best, as said above, postpone and hoist "L" or at least postpone and make an effort to notify competitors.  I've been bitten by this myself. Sailed a great race only to find out that the RC changed the course 2 minutes before the warning; Now I always check it just after the warning signal.
As an aside, I also find it interesting that nowhere in the rule is there a requirement to leave the course signal posted for the duration of the start sequence. It is implied, but not explicitly stated. From the rule a RC could post the course just prior to the warning, then remove it and replace it with another signal at some point during the sequence for a subsequent start.  Does the RC make an error by doing so? Not within the letter of the rule, but its really bad form. I only bring this up because I have seen it done.

I'm going to disagree with Eric Rimkus on this one, at least in a hypothetical case.
If the Race Committee displays a course and then changes it later without calling attention to the change and a competitor sails the original course, I believe that they ARE entitled to redress and that they meet the requirement of "through no fault of her own."
I believe that if a boat sees a course properly posted, then she can rely upon that information unless the Race Committee calls attention to the change, usually by displaying Code Flag L.
IMHO, failure to call attention to a changed course signal constitutes an "improper action or omission of the race committee" and I would award redress under the circumstances I described above.
Furthermore, I would expect the race committee itself to request redress for the competitor without waiting to see whether the competitor properly requested redress within the time limit and other requirements.

I completely agree with Clark Chapin in concept of what should be done, but I find no way to "get there" through redress.  The competitor failed to look at the course board at or after the warning signal and they could have done so. The RC did not commit a rule breech (by the letter of the rule) so is there an "improper action or omission"? Which brings up an interesting concept, must the RC break (fail to follow, really) a rule to commit an improper action or omission? Or does it suffice that they did something profoundly obtuse while following the rules to have committed an improper action or omission?

While I fully agree that the RC should never do such things and it is very poor race management, it happens and I just don't see a pathway to grant redress when it does barring some language in the SI.

There's another RYA Case which covers improper action vs non compliance with a rule, RYA 1969/12.

A race committee action or omission may be improper, even if no rule is broken, and even when it occurs before the
preparatory signal.
SUMMARY OF THE FACTS
About 15 minutes before the preparatory signal the race officer moved the starting line about half a mile from its original
location. In spite of a boat being sent to tow them, two boats arrived respectively four and seven minutes late for the start.
They started, and were the last to finish. They requested redress because the race officer had moved the line without a
postponement that was long enough to allow them to reach the new line. The request was refused on the grounds that the
race officer did not break the sailing instructions. The boats appealed.
DECISION
The appeals are upheld, and the cases are returned to the protest committee to award redress.
The race officer laid a fresh starting line without adequately postponing the start of the race to enable the boats to reach the
new position and to manoeuvre to obtain a good start. This made their scores significantly worse: it was improper, even
though it broke no racing rule or sailing instruction; and the boats were not at fault.
Request for Redress by Ajira and Goldcrest, Dale YC

"and it may replace one course signal with another and signal that wearing personal flotation devices is required (display flag Y with one sound)."

I still don't understand the quoted section above.  It seems nonsensical to me.  I presume that "replace on course signal with another" means changing the course, which is what our RC did.  But there is an AND in the middle (shouldn't it be OR?)  The second part about wearing a personal flotation device seems to have nothing to do with the first part.  Does the part in parentheses about flag and sound apply to the first part, the second part or both?   Really confusing to me.  

RYA appeals 1969/12 and 2008/2 (cited above) are two instances where a race committee did not explicitly break a rule, yet a competitor was entitled to redress because the committee's action was "improper". Of course, few (if any) US judges would feel bound by those appeals.
There are no World Sailing Cases that clarify whether an improper action needs to actually break a rule.
In the USA, I would grant the redress and, if a party to the redress hearing objected, would personally hand them a pre-stamped and addressed envelope addressed to US Sailing, Bristol, RI to facilitate their appeal.

David, the "replace one course signal with another" is important for "rolling starts" where the start signal for one class is the warning for another. In this case, the RC would have a course displayed right up until the start for one class, then at the time the class flag goes down and a new class flag goes up the course is also changed. It is a lot going on on the signal boat at one time when this is done and it is just another reason to avoid "rolling starts" among many especially if you can't designate courses for multiple classes at once. It also implies that the RC is to leave the course signal up from warning to the next warning if they intend to change it, but it doesn't specifically say that.  I think that is a problem with the rule as written.
The wearing of PFD (display flag Y) is also class specific. You may have a class where you decide not to require PFDs so no "Y", then at their start and the warning for the next class you decide that class is to wear PFDs, you would then display the "Y" flag and it would only apply to that class and any subsequent class if it is not removed at that subsequent class's warning.

I would hoist AP and C with sounds. 
No need to communicate with boats as L would require. 

Hoisting C would not be appropriate; this only applies "while boats are racing", not during a postponement.
Using L would be appropriate as it signals competitors to "come here" since you have new information to provide them.

Clark re: "would personally hand them a pre-stamped and addressed envelope addressed to US Sailing, Bristol, RI to facilitate their appeal."

Do you keep a box of envelopes and a book of stamps at the ready in your judge-bag? LOL