A tire with a shifted belt, bulge or a stiff spot in it can be balanced, but will still vibrate.
Any missing weights on the rear drums? Usually you can mount a drum on a wheel balancer to check.
Drivetrain angles could be off. GM had lots of rear tranny mount part numbers, but most replacements are generic. Basically, the angle between the tranny and the drive shaft must equal the angle between the driveshaft and the rear end pinion. This goes for up and down and side to side. A common angle gauge can be used to check. Of course angles can change with bad motor mounts, bent tranny crossmember (floor jacked or twisted from thrashing it), bad or incorrect rear tranny mount, bad rear suspension bushings. Bad body mounts may not change the angles but can cause a resonanace.
Had one case where the driveshaft was slightly bent. It was balanced, but still vibrated. I suppose the same thing could happen with a twisted one.
Putting it on a chassis dyno and observing underneath sound like a good idea to me if the solution remains elusive.
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