Have you adjusted the front band lately?
If not do that next and see if that helps the 2/3 shift
The other thing to check is the shifter linkage adjustment, you should be able to put the shifter in 2nd gear and remove the shift rod retainer and push the rod end up out of the shift arm from the tranny and see no movement on the arm, if that is good check 3rd gear engagement next. If either one move adjust the linkage so it does not move at all when putting the shift rod end into the shift arm hole in all 3 gears, reverse and neutral
I've had and race with many 727 T/A Cheetah reverse manual valve bodies in both the early cable shifters cars and the 1966 and later tranny, all of them shifted quickly clean when adjusted properly