Cracked Flex Plate

Your converter pilot should measure 1.81", and the 340 crank will have the a hole roughly the same. Measure both. According to my converter catalog in front of me, all 727s had the same size converter pilot. Different splines on the input shaft for sure in the earlier(pre-67) transmissions for sure. The 904 had two different size pilots, 1967-back 1.550", 68 and up 1.81".
Here's another shot, all be it a long one, was the engine originally in front of a standard transmission? I can't speak for Mopar, but I know when I worked for a GM dealer back in the day, GM had a crank for the automatic, and a different crank if the car had a standard transmission.
I would also think that if the transmission builder didn't install a pump bushing, it would have been leaking transmission fluid real quickly.
There is another issue that might be raising it's ugly head is the run-out of the converter hub. The shop I previously worked for aimed for about 5 to 10 thousands of an inch runout, while typical factory run out would be between 20 and 25 thousands. Just a thought.