Hi Matt,
I run a race like this. I've added the SI instruction that I use to identify the courses. I then add an amendment that will show all the start times for each of the three possible courses. I label them very clearly with very large numbers as to whether we are using number 1, 2 or 3. I am also very liberal with announcing the course number over and over again on the radio, especially if the course we are using is not the first course and the racer will have to turn the page to find the other course times. 
Good luck with your event.
8.      COURSES:

8.1     All boats will sail the same course. The course selected for the day will be posted on the R/C boat prior to the first warning signal. The starting times noted for the posted race number will be used. Be sure to use the correct start time sheet!

8.2     Course #1:   A(Start) – Zs – 24s – 22 – Finish(near 26)      [6.0nm]

         Course #2:   A(Start) – Zs – 24s – 21 – Finish(near 26)      [8.0nm]

         Course #3:   A(Start) – Zs – 24s – 19 – Finish(near 26)      [10.3nm]

8.3      All marks listed are considered rounding marks.  Marks are to be rounded to port unless they are followed by "s". 

           Marks followed by “s” are to be rounded to starboard. 

This is a very big (200+) open event:-
https://www.queenmary.org.uk/assets/Uploads/BM-SIs-2024-Final.pdf

And this an ordinary medium sized club's SIs.
https://www.islandbarn.org.uk/sailing-club/521/sailing-instructions-for-pursuit-races.html

Jim, you bring up interesting pursuit race instructions I am not familiar with! A pursuit race in San Diego Bay will have each individual boat, based on their handicap, given a start time. The ideal is that all boats sailing to their handicap over the designated distance will all finish the race at the same time! 
Matt, you might check out San Diego Yacht Club's website for their Hot Rum Race instructions. That is a pursuit race, although the course is always the same. 

Here are some examples

They are all 'fun', 'beer can' type events, based on PHS.  It's just not possible to get precise race durations to exactly match up with minute handicaps:  competitors have to take the rough with the smooth, but empirically, as usual, the best sailed boats usually win.  This may be less of an issue with PHRF TOD, where competitors are used to getting 'hard' handicaps, no matter how long they actually take to sail the course.

https://cyca-cdn-lkjnasdoiuasdjkhlasd.s3.ap-southeast-2.amazonaws.com/wp-content/uploads/2025/04/24113108/LGT-Crestone-Winter-Series-SI-2025-Final-1.pdf

https://drive.google.com/file/d/18dCzDGkWYSwIYY0TgLJX2B9Eo1836ZlU/view?usp=sharing

These two examples are quite big races with 80 to 100 boats spread over multiple divisions with different courses for each division so as to achieve a more or less similar target race time for all divisions.

It's up to the race officer to select the appropriate course and shorten course as necessary to get the race finished within the race time limit.

They both use a two 'lap' course, with a common start/finish/gate, and the second 'lap' somewhat shorter than the first.

Because of the complexity and the differences in courses and marks, while it is hypothetically possible to shorten by divisions and at various rounding marks using multiple mark boats, in practice this is not done and the race officer's only option is to shorten at the gate.

The CYCA race also provides for the race officer to designate a shortened course at the start of the race by displaying flag S with the warning signal, so effectively there are 4 possible lengths of courses:.

 https://cyca-cdn-lkjnasdoiuasdjkhlasd.s3.ap-southeast-2.amazonaws.com/wp-content/uploads/2025/04/30122832/Great-Veterans-2025-SIs-incl-Amendment-1.pdf

This example is with a smaller field, not using a gate, but still effectively with 2 'laps'

Thus if it's really soft the RO can shorten at CI, SIM, or LB first time round, or if it goes to a second lap, at SIM the second time round.

Matthew,
I wouldn't worry too much about updating handicap/starting number lists on the morning of the race to match the courses:  easier to settle on a target race time and handicap numbers, which can be done in advance, then match the course signaled to the target time and the conditions.

We run at the CBBC a yearly pursuit race based on a fixed time: generally, 2 hours with the slowest boat (based on personal progressive handicap) starting on the start gun and the fastest(highest handicap) starting last.  All boats finish at 2 hours after the start gun after travelling around a triangular circuit of about 5NM . There is no finish line: the order of finishing established by the boats with the most circuits and closest to the next rounding mark being the winner.  Competitors noting who they just beat and who they were just beaten by. It is a fun race with safer starts and exciting finishes as boats via for being closest to the next mark.  The handicap that each competitor starts (delay after the start gun) is determined from the BCE value as calculated by sailwave using the last race of a season long "long Race" Series  that they competed in by enetering a dummy next race and applying an elapsed time for all boats of 2 hours.   Last weekend due a likely severe weather event occurring late in the race we shortened it to 90 mins. An easy calculation using sailwave and transparent to all.
The NOR for the pursuit event makes reference to the club's standard NOR for the Long Series and general SI. It establishes hierarchy where there is any conflict. The advantage of this is that all competitors should be fully aware of the contents/requirements of the NOR for Seasons Long Series and note only differences rather than read the detail in another lengthy NOR.

I run a pursuit/reverse handicap race for a neighboring yacht club. 

I have attached the SI for this year's race. I use a program, Quick Score, which gives me the start times and will rescore if I have to shorten the race.

Matt ... one thing in pursuit races ... especially large ones ... is deciding how you want to handle OCS.  It is very common in these races to add SI's that apply a starting-penalty and state that boat "shall not return to the prestart side of the line".  (With the necessary rule changed and required citations)

I'm not sure how common this is.  At Rutland Sailing Club, we have a large digital clock/stop watch that is mounted on the committee (start) boat. Our SIs then include something like this:

A large digital race timing clock will be displayed from the committee boat. The clock counts up in hours:minutes:seconds from 00:00:00.  This clock, together with the display and removal of flags, will comprise the visual signals for starting the race.  This and the following amends Rule 26.

Competitors shall not start before the digital clock displays the starting time corresponding to the class of their boat.  The starting times shall be posted on the official notice board at least 1 hour before the start of the race and may be distributed at the competitor briefing.