First, let me say that I feel for you. I've got a 55 yr old house that is in good condition but needs some updating, and the bathroom is giving me them most headaches and I haven't even started yet.
I've got wall tile all around my bathroom too, leaks in the grout, poor venting, and galvanized pipe which needs to be replaced.
Let me start off by saying that very few things are impossible if cost is not a factor. If you want to salvage the bathroom and the tub you need to be willing to take out the ceiling under the bathroom. While it won't be easy to do, you should be able to raise the tub from the ground floor with the use of hydraulic or mechanical jacks. As I said, it won't be cheap, and you'll have to do a fair bit of searching to find someone to tackle the job, but you can probably find someone if the price is right.
You will likely need to raise the whole tub up, replace all the joists and supports and possibly the plumbing before you lower it back down. The plumbing should all be replaced, its just a question of doing it before or after the tub is lowered. You will need to be carefull not to raise the tub too high to avoid damaging your tiles if they are right above the tub, and you may need to remove them, which could be tricky.
As I said, most things can be done, you just need to find someone to do them and be willing to pay for it. I'd start by calling around, which you seem to have done, and even talk to the neighbours to see if they have had any similar experiences.
Good luck with it and let us know how it goes.
p.s. If you can find someone to raise the tub and replace the joists, be VERY careful. 600+ pounds of tub would make one heck of a dent in your kitchen if it came crashing down, not to mention what it would do to someone's head. Make sure the contractor has insurance and that they brace the jacks solidly. As well, you may want to consider inquiring about additional liability insurance on your property if you are having work done. I don't know if it's easy to get, but I'd rather have it and not need it than not have it and need it.