Hi there,
Well, your contractor sounds great! Today we are demolishing our 1949 bathroom and it is approximately 5 x 10. For labor only for the demolition, laying new tile, installing new tub toilet sink is $2800. I know the price is a bit low but we just had him redo the other bathroom.
Although my house is not quite as old as yours, my bathrooms had never been updated and the fixtures were worn out. I hated to rip them out, but the mosaics were chipping badly.
So far we are doing 3 bathrooms within 2 weeks of each other. I know it is insane, but we have lived here forever and the house needs help.
I can tell you that rerouting plumbing in one bathroom, cost me $3000 with the plumber. It was quite a bit of plumbing, we moved the toilet, moved location of shower and the tub and added another drain for double sink. The tiling for that job which was a 5 x 12 bathroom was about $2000 in labor.

The wall switch is inside the shower? Oh MY GOODNESS!!!!
Glad you are getting that fixed...nothing like being electrocuted in your shower.

I hope your remodel goes well. I can tell you that I'm working with several different people, hiring my own plumber, my own framer, sheetrocker, etc so I have lots of individual bills. All in all, with everything, I expect to come in under $5500 for everything, contractor, plumber, everything on the 5 x10 bath being torn out today, and that includes new fixtures. I'll let you know if I go over budget. :)