Where to buy a 727 transmission

I find it odd that the converter hub is giving all this grief. If the converter has been properly built, the hub checked for alignment with the converter body, there really isn't an explanation as to why the hub is wearing down.
I'm surprised that no one has asked you: how does the pump bushing look. Is it also worn out, cause if it is, it'll wear the hub out pretty damn quick. Also, do you have a leak from the front pump seal? How does the inner pump gear look? Are the tangs on this gear damaged in any way.

During the years that I worked in the industry, converter hub wear was typically the result of : pump bushing gone, broken flex plate, converter pilot(the little part that fits into the crank) out of round, hole in the crank not right, and last but not least, improper installation of the converter. I'm not saying you've installed it wrong, but I've seen guys not installing the converter all the way into the pump and then try to correct this problem with an air gun and socket upon installation of the transmission.

If you mount a converter in a lathe and spin it, you should find, using a dial gauge, the run out should not exceed more than 25 thousands of an inch. If it does, usually that means the hub has not been welded in straight, the two halves of the converter are mis-aligned, or possibly the converter has been dropped on the hub. Any converter shop that I've been into, the last step prior to balancing and painting is checking the hub runout.