No, the lockup torque converter didn't come along until '78, and cannot have accidentally been installed in your '64. It would be possible to make a lockup transmission to suit a '64, but it would require a great deal of deliberate and knowledgeable custom modification work.
Maybe there's something the matter with the torque converter, but before suspecting that I'd pay close attention to the band adjustments — both of them. How sure are you they're correctly adjusted and not too tight? The first two things listed in the FSM under "Transmission drags or locks" are "Kickdown band out of adjustment" and "Low-reverse band out of adjustment". The next two are "kickdown and/or low-reverse servo, band, or linkage malfunction", and "front and/or rear clutch faulty" — all possibilities here, as it seems — and then "Planetary gear sets broken or seized" (probably not; sounds like the transmission works fine other than this what you're experiencing) and "Overrunning clutch worn, broken, or seized" (also possible).