Don't forget definition Racing. There is no change in 2021-2024 edition. Boat is racing "...until she finishes and
clears the finishing line and marks..." Marks are important too.

In Scenarios 1 and 3, the mark figures in the boat's maneuvering to clear the line. Therefore she must pay a penalty and re-finish.
In 2, 4, and 5, the boat could go wherever it wanted to without the mark interceding in its decisions. She has/had finished.

In which of these diagrams has the boat ceased racing because she has cleared the finishing line?

None

Q&A 2006-002  covers when a boat 'cleared' the finishing line and marks.

I think one way I'd apply the Case 127 test would be to ask if there is a point at which the boat is outside the ends of the line and all finishing marks have been simultaneously left clear astern. From that point I'd say the boat is no longer racing. 

Diagrams 4 and 5 appear to meet that test (at least briefly, at about position 5.5), 1, 2 and 3 do not.

That is a fine test. But it is not definitive:  It must not exclude other tests.

Yes, I agree. I could see an example (like a downwind finish) where a boat was able to finish and continue sailing for some distance away from the line without going outside the boundaries. At some point you need to say she's not racing.

Or, similarly, like scenario 2 where the boat clearly finishes, has the ability to continue undeterred by the line and marks, then proceeds to sail off in an unseamanlike, bumbling manner unrelated to the race.

I've got no sympathy for the boat in scenario 2. I think she failed to clear the finishing line, was still racing and should be penalized.

Sympathy or no, Case 127 is definitive and clear. The presence of the finish mark did not influence the skipper's decision to bear off.
You are writing your own rule, contrary to governing Case.

How do I know that the finishing mark wasn't influencing the boat's choice of course? If she had bourne away more, or bourne away less, in an attempt to avoid hitting the finish mark, wouldn't she still be racing by the definition of the case? In positions 4 - 7 I could find that the boat was continually steering to avoid the mark (which is to say it influenced her choice of course) but ultimately failed to avoid it. If the boat sailed several more lengths to windward, well clear of the finish line, and then turned down and stupidly hit the mark I might agree that she had stopped racing. 

So in most instances I'd still maintain that unless a mark is astern or at least abaft the beam, it could potentially influence choice of course and the boat may still be racing.