I reread your post and I didn't answer all your questions. I think it is possible to modify a tempo within a movement; in fact it's written about Beethoven's playing that "each bar seemed to be in a different tempo."
That wasn't an insult, but it was an observation that he played freely and tailored the beat to fit emotional moods. If you listen to Schnabel's recording of this sonata, you will find this tradition alive and well, and not just in the second movement.
But you've reached the point where all pianists have to make a choice. The fact is, judges have their own problems. They are confronted in one competition with a lot of pianists, and they have to look for things to disqualify people from advancing. They cling to the objective; is it the same tempo all the way through? They almost have to. Also, many people out there, not just judges but certainly some, are very close-minded. They just think things have to be a certain way, and that's that. A pianist who feels a piece has to go a certain way then has to make a choice when playing before judges: betray thyself or play as you feel?
If you smooth out everything, and try and it make it objective and acceptable, you risk mis-reading who the judges are, what they expect, what they are listening for. You also risk sounding bland, which happens quite a lot in competitions for this very reason. If you are determined to play as you feel, you risk becoming mannered and trying too hard to prove something. You also risk disqualification, because if you are modifying the tempo left and right, it's not objective. It's subjective, and judges hate that. But on the other hand, unless you exaggerate everything, you'll come out having been true to yourself.
If I were you, I would listen to a lot of recordings of this piece. Schnabel, Arrau, Horowitz, Gould, Kempff, Backhaus, Brendel, there are tons of recordings. Get an idea as to when pianists get free with the tempo, and why.
Walter Ramsey