I have a 1990 Chevy half-ton Suburban, 5.7-liter V-8 with a four-speed automatic and 74,000 miles. For an extended time (four or five years) I have been attempting to eliminate a drive line "clunk" from this vehicle.
This is most often felt after coming to a stop, releasing the brakes, and starting off, such as at a stop sign. Sometimes it occurs as soon as the brakes are released, sometimes after the vehicle has traveled 15 or 20 feet, and even sometimes just as the vehicle comes to a stop with the brakes still applied. There is no definite pattern as near as I can tell. As I said, this has been going on for four or five years and is very annoying.
Some noises can really drive you up a wall, especially after four or five years. You've given a good description of the problem, but that still leaves a number of possible causes. I've pulled up a technical service bulletin from Chevrolet pertaining to a driveline clunk while braking on your Suburban (TSB #: 92-265-7A). It involves a special lubricant to be applied to the driveshaft slip-yoke splines at the transmission, to prevent binding after normal driveline tension. However, this only pertains to a single driveshaft application. If you have a double shaft with a hanger bearing we'll have to look elsewhere, but double check the yokes and the bearing regardless.
Go over the brakes very well. This may be the result of the brake shoes hanging up due to weak or improperly installed return springs. Brake drums that have been resurfaced too quickly act like a screw and pull the shoes away from the backing plate and snap back giving you similar symptoms, also.
After that I'd go over every part you can find in the suspension and driveline, looking for loose bolts or something worn out and slopping around. For example: transmission mount, transmission crossmember, leaf springs and anything else you can think of.