To determine which gears are in use try using the "OPERATING IN LO RANGE" section of the Owner's Guide as shown here:
https://www.pontiacsafari.com/55/Owners%20Guide.pdf
The car should start rolling in 2nd gear and downshift to 1st if the pedal is floored. It shouldn't upshift beyond 2nd unless you get to ~ 40 MPH. Compare what happens to when you take off in the LEFT DR position which should start in 1st gear.
Once we get more information I'll break out the HydraMatic troubleshooting guide.