I have 2 trucks. Both have a T5. Neither has an adapter plate. One drives like a new truck. The other has clutch shudder sometimes and I’m sensing some vibration at higher speeds.
I recommend that you go about solving this systematically.
Make sure the pilot bushing is within spec. New pilot bushings are cheap if there is any doubt.
Use a dial indicator to make sure the flywheel is perpendicular to the crank at 12, 3, 6 and 9 o’clock and that the rear of the bell is also within spec. This DIY that I wrote describes how to do these measurements.
T5 installation linkIf all that checks out, you should replace the slip yoke bushing inside the tail housing. The wobble should probably be a lot less than what you have now.
T5 parts vendor ALSTATEGEARThe T5 input shaft should not have any endplay. If it moves a little side to side, that’s ok. If there is endplay, then adding the appropriate thickness shim inside the input shaft bearing retainer will solve that.
The driveshaft angle needs to be correct. Typically, an engine crankshaft and transmission main shaft are pointing down 3 degrees towards the earth, front to back, on level ground. The rear axle pinion should have the same angle POINTING UP, rear to front. That way the pinion and tranny main shaft are PARALLEL, but usually NOT pointing straight at each other. It is my understanding that it’s best to avoid angles greater that 6 degrees.
Rebuilding a NWC S10 T5 isn’t very difficult and I can answer questions if you need help.