I adopted this fingering: 4312 first 4 measures and 4313 4313 for the other before you begin the sequence. then 4312 1432 4312 1213 and so on
no It doesn't seem to me that the combination of the fingering I use makes that you have to hit black keys with the thumb... do you have the original version by Rachmaninov? tha one in A minor or you got another one in other key? that's important to know...