First, I believe that the fingering is bad, I dont know why we would put a 3 on the second note of the first triplet. There is the fingering I would use:5 143 23 15 34 23 15 34 23 14 23 14 23 15In which triplet do you have more problem?Good luck and let us know!
Here are a few to try:Thumb on black keys, however the pattern with the hand fits rhythmically with the music.52, 4, 31, 42, 31, 21, 42, 31, 21, 42, 31, 21, 42, 31, 5Using 42 as opposed to 53 means less flexing and extending. 52, 4, 32, 21, 42, 31, 21, 42, 31, 21, 42, 31, 42, 31, 5Less twisting than what is indicated in the example.52, 4, 32, 21, 53, 42, 31, 53, 42, 31, 42, 31, 42, 31, 5
I think the fingering given in the score is the very best solution although perhaps if you have much "jazz style" fingering experience sliding the 4 will be very natural for the opening triplet of the RH i.e (15)4(24). The crossing (35) and (24) are the major players you want to master.This is not something that wants to be practiced without the Left hand. There is a particular feel that the (35) cross gives straight after the strong beat and then how it changes with the (24) and on the final beat the cross actually occurs together, this is better felt combined with the LH. It is difficult to explain in words the technique and what you might be missing but I wouldn't go changing the fingerings here. It shouldn't take many hours to solve this so I'm thinking the failure with the fingerings given here is a product of some technical inefficiency albeit subtle but enough to cause problems.