While it could be the TPS (throttle positioning sensor), as it is one of the sensors that your transmission monitors, I don’t think it is. Correct me if I am wrong, but you essentially said the problem started one day and kept on getting worse and worse, but you drove, your car, anyway. I know that you do need to get around and it is easy to continue driving, while ignoring a problem, but what happens when you do is that problem keeps getting worse until the device with the problem breaks down, just as has happened with your Impala.
That said, your mechanic IS NOT scamming you. Your Impala needs a transmission replacement yesterday or the day before. On re-reading your notes regarding your Impala’s issues, your problem started when you were driving to work. I suspect at that time, your Impala either threw a code (sent it to the car’s engine control computer) that indicated something had gone bad. On seeing the code, your car went into limp-home mode and stayed there. Your car was telling you something was wrong and asking to be fixed. However, apparently you didn’t have the Impala fixed and whatever problem was indicated by the the limp-home mode became worse, to the point that your car is now badly wounded.
A quick read of the possible causes includes damage to the input shaft and its gearing, damage to the torque converter and its impeller turbine, damage to the valve body and check valves and so forth. There are so many potential causes here that pinpointing it is quite hard.
That said, though, you can be sure your transmission is on the way to that big repair shop in the sky. Sooner, far sooner, than later, your car, instead of moving even a little, won’t be moving at all, quite possibly damaging other systems that are related to the transmission line. If that happens, your repair problems get infintely worse.
Now is the time to authorize the rebuilt trnansmission and have it installed. Your old transmission will come out and go to a remanufacturer, if it is reasonable shape, where it will be rebuilt for another motorist.
I can honestly understand your skepticism with your mechanic as there are so many horror stories out there that it is tough to ignore them. Your tech, though, was being honest with you, something that many mechanics are not when he said he didn’t know about transmission. However, he did know enough to know that yours was badly wounded. He might not have known the exact cause, but he did know the result.
My solution for your car is simple, have it hooked to a transmission shop and have the rebuilt installed. It should cure your problem.
As to the specific problem, I will venture a guess and say it is likely the torque converter as it is the major device that can go and shut down your car’s transmission in a manner similar to the one you described.
Let me know what happens, I’d be interested to find out.