My experience with CVT transmissions has been pretty horrible, overheating/burning fluid mainly due to lack of CVT fluid cooling capability causing valve body or valve body components to fail, I fixed by replacing the valve body myself for a couple of hundreds and spent another hundred for an aftermarket cooler and connections to help keep the fluid cooler. But this was on a Nissan and Nissan gets their CVT transmissions from a shitty manufacturer, You do not tend to see the same issues with CVT's from Toyota. Your issue could be something electrical in the transmission but it could just as easily be your computer going out, or a loose connection or wire in the harness. I had a dodge that started stalling when it got nice and warmed up, turned out to be a bad computer, I replaced the PCM but the new PCM was faulty and had an issue with the transmission communication, I tried backing my dodge up and the transmission was making all kinds of sounds and metal clanking, You would think the transmission was gone. I sent the computer back and got a replacement, and the dodge ran like a dream for years after that. I would diffidently try another shop, maybe a non-dealership shop, to take a look and try to diagnose it. There are shops that specialize in Asian model cars like Toyotech in my area that do good work and only work on these cars. Might save you a lot of money.