I have some recipes for stepping stones but I haven't tried them out myself so I hesitate to recommend them. I do know one way to get a perfectly smooth stepping stone that I have done myself. You could hold off using the ingredients you have and use them on another stone, but for this one, if you want to make sure it's perfectly smooth, you could buy a box of Diamondcrete. The last time I used it, I found it at Hobby Lobby and it was about $10. You grease the mold with Vaseline or mold release, lay your paper pattern down, face down, cut a piece of clear Contact paper to fit, lay it down sticky side up, then do your mosaic using the indirect method, (the backs of the tiles all facing up), pressing firmly to the Contact paper. Then you mix and gently pour the Diamondcrete. Follow the instructions on the label. It is super important that the mold is sitting on a flat level surface when you pour. The finished stepping stone will be completely smooth. You eliminate the need for grout using this method. It is more expensive than the usual method, but I used it when I had some commemorative stones to make on commission and they had to be smooth. How you lay the pattern face down is, you first hold it up to a window or on a light box, and you transfer the pattern to the reverse side of the paper, using a bold marker. That way, your pattern is reversed, your tiles are reversed, and then when you flip the stone over, everything is right side up. If you still want to try the recipes I have, let me know and I will post them.

This article says that although they have some of the same properties, and are both manufactured using a "sintering" process, sintered stone and porcelain are different.

Of course they like you! Point is as noted previously. I didn't say surgical. I can think your house reeks, or your outfit looks like hell, or your sofa is ugly. Doesn't mean I don't like you or I'm not coming to visit. I MAY talk to myself when I leave.....: ) I have one sister who quit smoking a decade ago.,another who smokes. They love one another, but it is an issue that the sister who quit, can not stay more than a couple hours. Kills her. Cat ownership means excellent maintenance, and I can tell you the cats appreciate it immensely.They are by nature, fastidious.

Are either of the tile store person or the contractor actually qualified stone installers? Or professional stone and tile cleaners? Limestone is porous. If you like, you can get a sample, weigh it, then soak it in water for a day to see it absorb water. Then take the sample and leave it in your current shower where you won't trip over it for a week or two while it accumulates soap scum. Try to clean it using only special limestone cleaners that you can buy from the tile shop.