I'd like to get a modern touch screen with Android Auto, etc. But with certain controls going through what's in there now, does that mean it's not possible?

 

Anything is possible, depending on how much $$$$$$$$$$$$ you have. Feasible? Maybe. Easy??? Super-not.
There are different improvements you can do, however. Check out this thread:
Replacement of HKS Camp2
and this thread:
GVIF / Chromecast mirroring
I did the first one and am happy with it, but have not hooked up the TSD controls. I have a wireless controller in my console for the rare occasions I want to change something.