That would be cool but unfortunately you are correct the converter will not work. The early 904's had an 18 spline input shaft and the 67 or so ups had a 27 spline input shaft plus a larger torque converter snout diameter. Your push button also would have a zero balance converter and you will need a balanced one for your 360.
Still, you should be able to find a reputable shop to modify snout and balance your push button trans converter to mate up to a 360.
Of course it will cost $
Pat Blais transmission is a good source for early to late modification
206-365-1966
