My 91 Park Ave Ultra starts hesitating around 55mph pretty bad. Although it hesitates slightly under almost all acceleration I especially notice it around 55mph. It happens simultaneously when when the transmission shifts around that speed. Could this be the TPS or does it sound like more of a transmission issue?

Could be a lot of things but I like to question tuning first.
Check Engine light on? / stored codes? How many miles on the 91 PA?
When was the last time you did a full tune up including plugs, wires, filters etc?
Have you even cleaned the throttle body or IAC ports etc..?

Is it supercharged or naturally aspirated?

And, same questions, mileage, service history, diagnostic trouble codes, etc.

Also, what octane gas are you using?

Ignition, 55 is when trans is in overdrive with clutch lockup-low revs, a weak spark will present itself here when you apply throttle. Check wires, plugs and that Magnavox coil pack.