In all likelihood, the source of the wobble is due to the weakening of the rear subframe mount on the unibody, induced by the narrow rounded top of the spacer, the height of the spacer, and the lack of a missing link. The unibody pad at the rear is just two thin layers of formed sheet metal with some nuts welded on. Your 2" wide spacers probably only have a contact area about 1.5" wide, and with rounded edges top and bottom. Being 6" tall creates leverage, too. Lacking a missing link allows the rear horns of the subframe to flex; the subframe may even already be cracked. The rear subframe also absorbs a lot of impact from the tires hitting the road or other objects.
Of all things, the missing link is perhaps the most important part. I know you've got one ordered, but you should also consider some other lateral bracing because of the height of yours and low contact area on the spacer. The welds you've applied are not sufficient.
This is what is possible without a missing link on an SFD'd truck (not mine):