HI -- How about a black slate with under heating matt.Or a tile that looks like wood flooring. You could go in any direction with the under flooring heating .

I will not recommend black slate, since I had a client once who had gotten done black honed stone (and slate is always without polish) by someone else and ended up changing it, since, according to her, it would suck the lights out completely and was depressing to get ready into.
Like you said going with marble with be no brainer but if you go with a pattern in marble, and there are beautiful water jet patterns available that can be shipped to you. I will suggest you to conact manjari@ollinstone.com . She can help you design it, if you send her your floor plan.

Try taking one of the gray shades from the marble to use on the floor, ( maybe with a slight bluish or rose tint if you like). Don't use marble. It's slippery and will not wear well. The marble is beautiful and oftentimes reasonably priced but you will regret this choice. It is overused currently by contractors and will date your bathroom. Go for a matte finish. Avoid shiny.

How about a honed or tumbled Carrera in a basket weave pattern? The basket weave is available with color dots.