I think it should be possible.
It sounds like you're already most of the way there, except you're having trouble getting everything to line up as far as the measures and beats?
One idea is to just record the style, as it sounds like you're doing, then use the piano roll editor to adjust things as needed to make everything line up as desired. As long as you've got the PSR-S950 and Cubase set to the same tempo and time signature, any needed adjustments after you've made the recording should be fairly minimal.
I don't have a PSR-S950, but later tonight I'll try it with my PSR-E443 to see what the best procedure might be.