I like the idea of subway - but why not a fireclay subway tile. I think that would look very pretty .

I'd remove that short back splash before doing anything. It will not look right.

I too am not a fan of the short backsplash. However, people do keep them and tile up the rest of the way. Again, not my preference, but it is your kitchen. Yes, a glass mosaic would be too busy.

Don't do the limestone that you are showing, for a few reasons. First, it is a dated look. Second, you never know what run you will get. Yours might turn pinkish when installed, And three, I think even when sealed, some people still have staining behind the sink area.

I like your idea of matching the color of the floor. It seems to go nicely with the counter. I would do a ceramic tile in the lightest color of your backsplash.

I hadn't thought about removing the Quartz backsplash.....hmmmm....

How hard is it to remove that without damaging the countertop? Is wall repair usually necessary?

Full disclosure: I don't like tile back splashes. What you have is perfect. If you insist on tile you really should take out what you have.