Well, I never thought a simple question would generate such a huge amount of comments.
I am a simple guy, and finding an easy answer is always my goal.
The RO sets the course, gives a fair start, follows the evolution of wind, current, conditions, and fills the arrival order. That's more than enough to be done properly.
In any case of troubles about RRS, RO should immediately leave it to the PC.
If a hearing in the protest room takes 10 to 20/30 minutes, it's because hearing the parties, establishing the facts, and making a decision takes a long time. That time, on a moving boat, with another race behind, the RO doesn't have it.
And whatever the decision of the RO in that case (NSC, DNF, or let it go as it is), if he doesn't feel confortable with his décision, he can protest it and leave it to the jury (thanks a lot, officer !)

A lot of chat for a rather simple case.

To me... there are 2 halves to OPs question...

1st half - was Red racing?  Yes.  Her stern was still on the finish line when she broke rule 10.

2nd half - Did Red tack and gybe in accordance with 44.2...namely 'promptly' after the incident? This question is subject to the protest system, just like any other allegation of a breach of a rule not exonerated.

So the RC registers her second crossing i.a.w. Finish (a), and if anyone (RC or another boat) is unhappy about it, they can protest her for not exonerating 'promptly'.  Otherwise her 2nd crossing finish stands.

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As for the r23.1 discussion, Racing is a time-block from time-a to time-b.  Once you pass time-b it's over.  You can't restart.  If Red had met the interpretation of Case 127, then she was past time-b.  Not racing.

If a boat not racing breaks a rule, then apply RRS 60.5(c)

If a boat has broken a rule when not racing, her penalty shall apply to the race sailed nearest in time to the incident.

What am I missing?

Yes you can only postpone before the start. You can do it in the last second. 
You start when the flag is removed so, if this had a few seconds delay, the start would be late but there is the posability of postponment. 

Just follow the procedure and be practical. 

But, unless I am misreading the original post, the “restricted finish” in this case is 2/3 of the way up the course and nowhere near the starting area. The only boats playing in that area are the 18s and the H16s would only be there when finishing. So, again, I’ll ask, what issue are we trying to resolve by restricting this finish?

Agree.  As long as it's getting our of RRoS ok.