Just to be clear - those boxes shown in the first photo are on the floor - not on a raised hearth - correct? When I read your post where you've added that the bottom stone is staying the same, I assumed that there would be a slab on stone used on/as a hearth. After seeing the AI images, I assume that the "bottom stone" = the tiles on the floor. If that's not correct, please let me know.

What is the stone that's being used on the FP (some kind of travertine?) + what is the stone that's been used on the floor?

Your floor tile would look dramatically different if the grout lines (and the tile itself) were deep cleaned. It's not difficult to do if you use:

The Pink Stuff (paste form) - available at Target/HD/Amazon/etc.

Plus, a cordless rotating power brush:

Many on Amazon + other retailers. Both of the above products work on their own - however, combining them makes it easier to do and improves the final result.

Once the grout + tile are clean, it will change the overall "color" of the tile.

Obviously, the tile color also looks different in the above example due to when the photos were taken (at night w/ overhead lighting + during the day with natural light).

I helped my sister clean her 12x12 travertine tile/grout lines - it made a significant impact on how the tile looked (color of tile + greatly lessened the "grid" look).

The results were similar to the ones below (except not quite as dramatic as the below before/after photo:

I would want to know what the original color of the tile/grout is before I made selections for a surface that directly meets the floor.

Unless you don't plan on ever deep cleaning your floor tile/grout - quite a few people don't ever deep clean their tile floors/grout lines.

I'd choose the Pale Umber, the Bone looks too white and bright.

Keeping the grout similar to the brick or tile makes the stone look better, the bright contrast just shows off the grout.

I like grout to not be a contrast so the umber for me too.