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I was considering using floor tile in my tank in place of a loose stone or sand substrate.

Would ceramic, porcelain or slate tile be safe in the tank?

I've used slate tile as a dock material before, so its not unsafe for turtles. the biggest concern for it as a substrate (from what i've seen) is that so much bacteria can get trapped underneath it. much like when using large rocks, dirt and poop can get stuck under it, and unless you want to be pulling them out and scrubbing them, its not exactly ideal. since they're heavy, there's also risk for your turtle moving them around and damaging the tank.

My thought was to actually set them into the tank permanently with adhesive silicone which if done right should effectively seal the underside of the tiles and prevent their being moved.

Something like this, with tiles across the entire bottom of the tank and then a series of broken/cut tiles stacked up into the corner.

No matter how well you try to seal it, some waste will always get under or between tiles in areas that the silicone didn't get to. What don't you like about sand and/or stone?

I actually work with silicone every day as part of my job.

If I level the tank and pour a 1/8" layer of RTV silicone to coat the entire bottom of the tank and then set the base tiles into that, press down, wait for the silicone to cure and then trim the excess from between the tiles and the edges it should create a water tight seal around and under the tiles that will last basically forever.

Problems I see with larger river rocks are the need to remove, scrub and clean them once or twice a year. Sand has a similar issue and would potentially complicate vacuuming the tank.

A sealed tile "floor" would be as easy to clean as a tank with no substrate at all while having a natural stone appearance.

I use a ceramic tile in a basking area in one of my tanks. You have a pretty cool idea, but it will make tank resealing extremely difficult. You could do a bare tank and add a background underneath the glass. Maybe even a window cling inside.