It only takes a few minutes to pop the yoke off the driveshaft, and requires no special tools. Grease the splines before you install it and it will stay on there.
AJ/FormS has the right idea here to make your quick test with the drive shaft disconnected.
Take the yoke off of your existing drive shaft, pretty simple. Grease the removed yoke splines and slip it on to your transmission tail shaft.
Now you can do your test right here, right now without having to buy parts and the many days of delays finding a used spare yoke. 7260 U-Joints are readily available also for putting the yoke back on the drive shaft if you need a new one.
These 727s have 2 bands that can be readjusted too. If you can find someone locally who knows how to adjust these 2 bands. If these band adjustments are way out of whack, it would suggest more serious problems. If they are within specs, all the better.
You could do this band adjustment and see if it makes the internal noises better or worse. Another piece of the puzzle . . .
