Some movement is ok. If it's really bad, you may have bigger issues. Like your engine mounts are shot or your driveshaft is either unbalanced or going bad. Vibrations can be the cause of bad motor mounts, hence all the vibrations getting put on the tranny mounts. A warped driveshaft which feeds into the tranny can also wreck havoc. Is the driveshaft still stock? Have you noticed any clunking coming from underneith and from the rear when under initial load????????????
Tranny mounts are pretty simple and inexpensive to fix. Engine mounts require lifting the engine a little and you're looking at 2 hours in labour on that. A bad driveshaft is an easy fix. Labour is $25 roughly, however aluminium shafts go for around $300 these days.
some like to pry on the mount with a lever - if the mount allows movement with a prybar, it is shot. if doing the trans mount, i might hit the motor mounts too (that sounds like more of the issue to me, but i am not there with you). if one mount went south, others are likely not far behind.
It doesnt seem to be the drive shaft. It only happens if I drive hard and only after shifting. When I shift at higher RPM its feels like I really am just abusing the tranny. Im not power shifting or anything crazy, just driving hard. Passengers can rally feel the jarring. its like a double wiplash, first from taking off, then from the excessive jarring from the shift. I will try the crowbar under the car. Is their a way to test engine mounts. I have a lift so replacing those wont be to bad.
with the motor mounts: do you have a stock mech fan? if so, look at the fan blade-to-shroud orientation. if the fan is sitting low (almost hittin the bottom of the shroud), that suggests the mounts are worn (a tell tale).
i would go with poly or captured mounts (as your 93 should have). the captured mounts were used on verts originally, but later (by 93) used on all 5.0 stangs. it is a better design, IMHO.
you could be like mine was. Only bout 1/2" left on the thread was left to hold it the mount on. loose big time. but now i have the FMS crossmember and energy suspension for the sides of the member and the tranny mount itself.