Has anyone really put much thought to what the difference between DNF and NSC is?  Well, it's there in Appendix A10, isn't it?

DNF Did not finish
NSC Did not sail the course (other than DNF)  

So NSC is Did not Sail the Course when did Finish.  Or simply put...:

DSC(DID NOT FIN) = DNF
But;
FIN + DSC = NSC

Ang and Giff's Application logic #3 above relies on the conclusion that Boat A 'did not finish'.  Ok. Fine.  But the 'did not finish' (DNF) then makes NSC un-usable in this case., per A10.  (DSC(DID NOT FIN))  That's why I don't agree that NSC is the 'according' score.

So we are back to square 1.

Either score her FINished when she crossed prior to the turns, or score her DNF which relies on the judgement of Boat A's purpose of doing turns which is based in turn on the judgement that there was a rule breach.

I would say FINished is safer than DNF.  Then [wait for a] protest for the mark touch.

This preserves the underlying principal being that critical determinations of most rule breaches, penalties and exonerations are sorted by the PC after a protest. Rule 31 being such a rule.

This is different to when a boat crosses the line, crew fist bumps and high-fives each other and the beers opened, but RO noted she missed Mark  2 and rounded Mark 3 on the wrong side.  That's FIN + DSC = NSC for sure!

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.