Check the driveshaft and u-joints for any play. My truck did that until I replaced the center bearing on the d-shaft, not sure if a k20 would have that though.
It might be the spider gears, sorry to say it but Ive had similar problems, sounds just like a u-joint. Pull the cover make sure the pin is still riding in the midle-even more important is the 5/16 head bolt that holds the pin to the carrier, if its not there, get a set of spiders ASAP if you catch it soon enough it wont destroy the ring and pinion.
u got a back u joint problem go under ur truck shake ur drive shaft if there is movement in it check n c if it in the front or the back...oo yeah u joints suck good luck....
