Drum replacement via midi substitution/problem wth alignment

Hello, I am involved in drums replacement for a project, so I take the hitpoints of the drum tracks, create midi notes, and assign them to drum samples to blend together with the original audio. However, when I bounce the midi tracks, the alignment of the new drums is not accurate, and leaves hours of manual adjustment. The samples bounced to audio tracks should stay underneath the original track I presume.

Could you please help me find a solution to the problem?

Many thanks!