I'm not surprised about the quotes. I see some really high tiling prices and you can expect a condo tax. They are a pain to work in.
Sorry, I thought I understood the situation but I got confused with "floor tiles..twice as thick as wall tile.."
I don't completely understand why the thicknesses cause an issue if they are on horizontal and vertical planes. But I likely am misunderstanding something.
I also don't have much experience tiling over tile but Sven may, he seems to have a really good grasp on the subject. If you do get down to underlayment, so long as it's an appropriate material, get it as smooth as you can, understanding any corners cut here is kicking the can down the road to when you start laying. But there is a built in tolerance as well due to the mortar bed. Sven had a great point about now being the time to add a heated underlay or trace. I've ordered a kit from Amazon a few times and it was easy to install. But like you mentioned, have to keep an eye on the elevations as well. Schlueter (and likely others that I don't know of sell) loads of transition strips to accomodate different elevations across thresholds but best to figure this all out well beforehand
For some reason, I assumed that wall tiles might be thinner than floor tiles. I don't know the item numbers of what they purchased, but just did a quick visit to the Lowes website and found that tile thickness can vary between item numbers. One style of subway tile I checked was actually slightly thicker than a floor tile that I randomly checked.
What is an acceptable difference in the floor elevations transitioning from the bathroom to the adjoining room? I realize it should be identical, but what is considered "acceptable"?
When I examined the present elevation difference the hall was about 1/4" higher than the tile in the bathroom. If the new tile/thinset thickness is 1/2", that will reverse the 1/4" indifference. That's what I'm hoping for.
Tiling over tile, in general, I don't prefer it, because I want to be absolutely sure of the subfloor and underlayment, since I want the floor to last.
But not having seen it, I can't say for sure. I would look very carefully for cracks in the grout or any other signs of movement.
You won't really know how hard it will be to demo the existing floor until you do it because you won't know how it was constructed until you get in there. I'd say the older the building the more difficult it will be. Usually ninety percent of it comes out easy and ten percent is near impossible.
Another reason to remove it all is so you can build it up to plane out flat with the hall floor. As for "acceptable", I'd say 3/4" is the max, but definitely not ideal. You want the transition to be under the door. If the hall is a wood floor I would make the transition out of similar wood, if not you can buy lots of different transitions.
You can get backerboard in 1/2" and 1/4" sheets. You should spread thinset under the bb as well.
You can also get a 1/8" uncoupling membrane (Ditra, from Schluter) in lieu of backerboard on the floor. It's orange and comes in different length rolls approx 3'wide, you can cut it with a utility knife. It's a little harder to install as it wants to roll up at the ends, so I weigh it down. It's vital to get the right spread of thinset under it because it has no fasteners.
One cool thing about it is that it has indents on the surface where you can place the "warm wire" for underfloor heat. I use a hot glue gun to stick the wire in place where needed.
If you do tile over tile you'll want to clean/scuff/abrade the existing tiles well and use a modified thinset for better adhesion.