Engineered Jatoba would work over radiant heat. Trying to match with synthetic will be very hard.

Before you worry too much about the product (laminate or vinyl), you will need to remove the tile WITHOUT disturbing the in-floor radiant heat. I'm going to guess the tile is sitting on radiant wires and not hydronic tubing.

To jack out tiles without disturbing the wiring is SUPER DIFFICULT. I'm going to bet you will lose the radiant heat source simply by removing the tiles. Of course I'm only assuming you have radiant wires. Can you confirm what format of radiant heat you have?

Jatoba aka Brazilian Cherry

Have you considered carpeting? This article is interesting and it tells precisely what underlayment to use.

I think stain resistant carpet on the second floor/hallway and bedrooms, in a coordinate color to the stairs would be lovely.

Hi, we have the hydronic tubing and my husband is not willing to have the tiles removed.

I wasn't sure if I could use carpeting with hydronic radiant flooring but I would definately prefer that. You had mentioned an article???