The transmission in both cars should be the same transmission. For the Special, Skylark cars though , basically there were three different ST300 transmissions. There was a MJ model for all 300 v-8 models , except Sportwagon. The Sportwagon used a MR model transmission. I think the difference was that the transmission for the Sportwagon had a long tailshaft. Internally these two used the same torque converter, valve body plate and same number of driven and drive plates in the both reverse and forward clutches.
The third ST300 transmission was for all v-6 engine and the model was LS. It had a different valve body plate , identified with a notch in it , a different reverse clutch pressure plate and reverse clutch piston. Also the number of driven and drive plates was one less than the transmission used behind the 300 v-8 cars.
From your description, it sounds like an issue with either the idle stator switch being out of adjustment or an issue with the stator valve body or solenoid .
The purpose of the idle stator switch is to reduce engine creep, by changing the stall speed of the torque converter. By changing the stall speed, it makes for less force needed to be held on the brake pedal when stopped.
My thought would be to check the adjustment of the stator switch first.
My thought process may be flawed here, but thinking about your issue, a cold engine and transmission would have a heavier transmission fluid and create a bit more pressure internally. As the engine and transmission warm up, the transmission fluid would thin, resulting in an increase in accelerator to get the car to move.