OK mopower440 good diagnostics so far, getting to the bottom of it.
Here is a picture of a 727 tail shaft, there is a large ball bearing that installs by the key in the picture.
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You could take the speedo gear out and have your grandson turn the rear wheels again, then you can see if you can feel (or see) that bad bearing by carefully touching the shaft at the speedo gear grooves as he turns the wheels. That large ball bearing is real close to the speedo opening in the tail case. May be able to feel on the shaft that it is further up the line into the transmission more like at the Planetary Gears on the trans end of this same shaft.
This is one thing to check before we go further, that bearing can be changed just by taking the tail shaft housing off if it is noticeably bad.
Was talking with my guy Brian that builds all my mopar trannys. He was saying that he doubts it is that large tail shaft bearing and more than likely the Planetary Gear Assembly. He was saying that the Panetary Gears can get lots of slop in them.
The guy that built the trans probably put new clutches, and new bands in it but probably reused the used planetary gear setup and that is a good chance why it is failing now . . just wore out. Unfortunately the transmission has to come out to get to it.
On to the next tests . . .
Can also drop the trans pan and see if there is lots of metal shavings in it, if so take the trans out and replace the faulty parts. They are one of the easier automatic transmissions to rebuild.