Your photo is not showing up for me.
While I can't answer your question, I would suggest that you cross post this question on the kitchens forum and the bathrooms forum to the attention of stonegirl or Bill Vincent. They respond regularly over there, and I bet they could help.

Thanks kimkitchy. Here's the link to the photo of the floor:

I also posted in flooring. I really wanted to try and save the floor to keep it original to the house but I am not having any luck with finding anyone to help. Restoration people don't return phone calls or email since I don't think they want to deal with residential work and the carpet/flooring people don't quite know what to do with it. Most of the comments I get are to remove the surface/sand blast it/jackhammer it all out and then use a leveler on it and start over with another floor.
I think the efflorescence is the biggest problem in that it could keep coming back up. It seems such a shame to cover up all that beautiful red, purple, blue, green and gray slate (which looks just green and brown in the pic because of the yellowed surface).

As you can see below, stripping old acrylic or urethane finishes off slate is no simple job. And the joints could be a real problem. Best to have a stone setter look at those before you expend any effort or money stripping the stone.

Here is a link that might be useful: Care and Maintenance of Slate Flooring

WOW. I would want to keep that floor too, if I were you. Sometimes what we can't get done right away, we simply live with until we can take care of it properly (or afford to). In the end, if you did have to take it up, maybe you could use it for a patio or re-lay it in a garden room or use it for some other purpose. (Hope you find a way to keep it where it is though).

Thank you kimkitchy and worthy, especially for that website explaining urethane removal from slate floors. I have contacted a couple of floor restoration/cleaning companies and will see if they can help me. This is too big of a job for me to diy.

Hi- i just came across your post while looking for a solution to my problem. Which is very similar to yours! We removed ceramic tile from our mudroom in our MCM home. It was really easy to pop up and guess what was under it all?!?!? Yes!!!! Gorgeous slate tile! Very similar to yours! We had decided to invest in a couple bottles of cement/grout haze remover, sulphamic acid and a couple cans of good ole elbow grease! We still have a lot of efflorescence to work on and some tiles that need to be replaced. (A lucky stop at our local Restore resulted in 30+ tiles to use! We don't need that many but for $6 ...) I have a couple of questions and I am hoping that maybe someone might read this and be able to help.

If I recolor the grout will it keep the efflorescence from reappearing?

Also the tiles still have a faint bit of efflorescence/grout haze that i just can't get to go! They look great when they're wet soooooo will sealing them keep that haze at bay?

swickbb- I hope you had success with your floor!

There are special acid washes for removing the efflorescence from grout. Contact a retailer specializing in stone. If the efflorescence continues coming back there's some moisture problem that may have to be addressed. Or maybe cannot be cured if, say, the mudroom is on a thin slab rather than over a full basement. I've put down down slate in new basements and first floors with no problems.

We had a similar slate floor put down in our dorm apt in Maine. It was on a slab, and we never had any problems with the floor. Once a year, my late husband would wash it thoroughly, let it dry and then re-seal the slate. We had it for 8-9 years while we were there.