Bands may be slipping? Help please

1965 Barracuda, 273, 904 auto. Was parked for about 5 years and just got it running again. I think something feels funny with the trans:

New trans oil and filter.

When accelerating, especially when going from zero up to about 40mph, it feels like it shutters. The car shakes a bit, but if I let off the throttle and ease into it, there is much less or no shutter. Feels like a trans issue, but not sure. Any ideas?


Thanks for your input,

Rick