How difficult would it be to convert a regular US-style shower faucet into a thermostat faucet?
It already is that.

That's what that handle is.  Depending on the type of valve, it is either


a thermostatic control that you rotate left/right to the desired set temperature (no choice of flow), or 
a joystick, in which left/right is thermostatic control, and in/out are flow control.  Rather like a Delta faucet. 


Build like a Victorian

The knotty problem of backside access to a tub faucet is one the Victorian-era builders were well familiar with.  It was "on their watch" that indoor plumbing leapt to popularity.  They had a clever solution: Put a cabinet door on the backside of the faucet.  In my house I can trivially access the tub-faucet backside.  It's trimmed like a perfectly civilized cabinet door, and provides full access to valve backside, trap, and supply plumbing.  Changing the tub faucet, drain lever or trap is a 20 minute job, and yer done. 

A more cunning installation might put a bookcase there with a removable back, for instance.