I would not try someone who's income depends on making sales. High gloss floor tiles especially for bathrooms are not ideal since they lack grip once they get wet or when the bathroom is moist after a shower.

First be okay with the fact the bathroom tiles might need to be replaced. All of them. Replacing them in the bathroom will have the least impact on the rest of the house and whatever comes out in one piece, can be stored for future cracks. Maybe you can find a similar color but a different size, so it won't look too awkward, just an idea. Taking out a cracked tile is quite easy. Put on some gloves and safety glasses and (carefully) smash the broken tile with a hammer. An old screwdriver or chisel will help you tilt the pieces out. Work from the hole outwards to remove the other tiles. Removing a good tile is nearly impossible. Assuming it is still glued firmly, I'd say impossible. But, if you want to try anyway, you'll need to mill out the grout and then figure out a way to lift the tile..

If you are looking to keep the "period" look, then I say no. My place is from 1916 & had a gross 1980's reno. I ripped out all the ugly vinyl floor & cheap Sears sink & went with a black hex floor, white subway, dark grey grout on both. Toilet & tub were original, but I got an old "Standard" wall mount sink with chrome legs & towel bars & an antique medicine chest, light fixtures & glass shelving & towel bar off Ebay. My total job...about $5k. Help my tile guy is my neighbor, but those 10, 15, 20k bathrooms were out of the question.

I'm finding it a little hard to see the detail. Can you enlarge the top 2 plans?