[Greenbuilding] Redoing all floors

[Ktot (g)]

I have a brand new home (finished mid-May) that is completely off-grid. 
Solar and wind power, solar thermal radiant heat and hot water, and passive 
solar design.

The problem--the stained concrete floors and countertops are defective. The 
countertops should be an easy fix--sanding and applying another layer of 
epoxy. But the floors are very problematic.

First, the supposedly very experienced contractor who did them is refusing 
to take responsibility for their defective work--they didn't allow the 
concrete even 1/2 the curing time required--but my attorney is addressing 
that.

My question for the list members--any thoughts on redoing the floors? I had 
been planning to do stained concrete again but am now leaning away from it, 
leaning towards ceramic tiles. (Re stained I've looked at redoing 
water-based stain, doing acid-based, and doing grind and polish. If 
water-based, at least, I'd probably have to go with overlay. The original 
was just regular water-based staining except overlay in the bathroom. The 
concrete is regular concrete, not gypcrete.)

My requirements:
1. Great thermal mass as they are the sink for the sun's heat in my house.
2. Very durable--I live in the mountains, am in and out all day with 
multiple dogs, have a lot of gravely/rocky grit that comes in with us
3. Very easy to maintain
4. Can go over the stained concrete (which has been cracking due to the 
house settling) with minimal hassle. I do know the sealer at least has to be 
removed, and also the concrete isn't level--with a five foot level, in a few 
spots there's a full 3/4 in. variation

Also I have radiant pipes in the floor but a normal thin tile or similar 
covering shouldn't negatively impact that, I believe, as the concrete layer 
is only 2 in. thick.

Any suggestions?