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My 79 f150 4x4 with a c6 has a noise with a definite feeling as it happens. It happens after going from reverse or park to drive and then accelerating. You can feel a kinda slip and then kachunk. It seems to have gotten a little worse since put new leaf springs in the rear. It's not lifted and the suspension has not been modified. I have looked at and tried to see if there is slop in a u-joint but haven't been able to find anything.
Maybe not so much slop in a U-joint, but maybe slop in the rear end itself. Block the rear tires, and put the tranny in neutral and try turning the drive shaft by hand, and then side to side. Sounds like your tranny is taking up slop in the drive train farther down before it drops in gear.
If I understand you correctly I had the very same symptoms about 15 years ago on my 78 F150 and fixed it.
If you haven’t found your problem yet and are interested:
First, get someone behind the wheel and set up the scenario to cause the clunk with you safely on the ground, out of the way, with a view of the driveline. As they accelerate watch the driveline to see if it skips (like skipping a tooth on the ring gear inside the rear end) at the same time you hear/feel the clunk.
Second, find out if you have a Ford Trak-lok differential.