Ah, so, grasshopper- - - - - - -the "Terrible-Glide"! They were notorious for poor performance and difficulty to rebuild back in the 1950's, and I'm sure 50-something years hasn't improved that situation any! Proceed with all due speed to the TH 350 option!
Edit: Your "cast iron case" comment didn't sound right. I was pretty sure I remembered the TG as Chevy's first aluminum case transmission, and a little research proved that to be correct. If your trans has a cast iron case, it's a 1st.-generation Powerglide. PG transmissions didn't switch to aluminum case units until 63 or so, and TG never had a cast iron model. The TG also has a removable oil pan, something the cast iron PG doesn't have. Turboglides had a 3-stage torque converter, and they didn't have a discernible change in RPM between shifts, sort of like a downsized and less-robust version of a Buick Flight Pitch Dynaflow.
Jerry