I had this very same problem. I broke 3 or 4 plates before I checked for the trans bellhousing alignment. Here is the break down. The centerline of the input shaft of the trans is not aligned with the centerline of the crank in the motor. Oddly enough my trans was a small 727 as well. What I did was take my trans to a trans shop and have them take all the internals out of the trans. Then I mounted the case back in the car and mounted a dial indicator to the flywheel flange on the back of the crank (without the flexplate installed). Rotate the motor over by hand and watch the dial indicator for movement. Anything more than a .002 variance is bad. Most people dont realize this can be a problem. My trans guy stated that this problem is more common than most people think. What people regularly do is put a stout full circle flexplate on it and eventually that wears out the thrust bearing in the motor or the bushing in the front pump of the trans. To remedy this problem, Lakewood make offset dowels to relocate the bellhousing. This is a popular thing to do with 4 speed cars that run a aftermarket bell housing. Once I corrected my alignment issues it never broke a stock flexplate again.