Change the offset to 686, i think it will sound better. The bpm is right, but it's a ternary rhythm so you have to use 1/3 (or 1/6 or 1/12) in the beat snap divisor.
SPOILERthe beat snap divisor is this thing :
it's in french tho Sadly, you will have to resnap all the object :/
The saxophone part is kinda arrhythmic (it's jazz after all) so good luck with mapping
Hope it helped