I think I may have figured out the solution to my issue.
In measures 43 through 44, though it's extremely difficult, it seems like after a LOT (!) of careful practice it may be possible to play the tremolo in the bottom notes as follows: 4-2 on A-C and 5-3 on G-B flat, all while the left thumb plays the moving eighth notes (D, E, D, F, etc.). This is very difficult at tempo, but I guess it's possible. I'll work towards it very slowly and carefully, being sure not to strain my hand.
In measures 45 through 48, I had been trying to use 4-2-1 on A-C-D and 5-3 on G-B flat, and it just seemed impossible leading up to quarter note = 100 (and it needs to be at quarter note = 126, so not even close to tempo). I just realized today that this isn't the way to go, and this should have been obvious from the outset. The thumb should take the two adjacent white notes. Therefore, the fingering for these measures should be 3-1 on A-C-D (thumb on C&D), and 4-2 on G-B flat. This is still a little awkward, but much more sensible than the fingering I had been using and allows better endurance, since it switches the fingers used in mm. 43-44.
Measures 57-58 are very difficult, and the left hand is very similar to measures 43-44. The same fingering should be employed - except now the thumb of the left hand is playing different notes, so the stretch is a little wider. The right hand is very tricky here, but only one fingering is really possible, so I'll just practice it slowly.
Darn you, Stravinsky!! You must hate us pianists (apparently), but your music is marvelous anyway. I can't think of anything as difficult as this movement except perhaps Liszt's 'Feux Follets' or one of the other super-virtuoso pieces. A long road of practicing is ahead.....