'60 LeBAron, update, do I adjust the transmission cable???????

I have got the '60 LeBaron moving again, but it does so grudgingly. While I have not driven much over 100 feet, it seems to do just fine once in gear. I have to start the car, run it a few moments, and then push buttons and wait. Sometime waiting about 40 seconds or so before it responds, if it responds. Sometimes I wait, give it a little gas, and it will pop on, usually with a lurch due to my giving it gas. Reverse is the worst. Drive is poor going into gear, but ok. We discovered when rebuilding the top of the engine that the motor had been overhauled. The transmission is sprayed the same color so we know it too has been out of the car at some point. Now whether it was overhauled or not, I don't know. As I said, it seems to do fine once in gear, the fluid looks fine. We are considering adjusting the linkage cable/wheel. Has anyone ever had to do this? What were the results? I just don't want to tinker with something if it is not likely the cause, though we think it is.

The car is leaving tommorrow, by truck, to the shop for exhaust, rear brakes, and installation of a correct working power brake booster. If a new brake light switch gets the lights functioning, then I may try to drive it home................