I mount my thresholds on whichever material puts them on an acceptable level with the tile. I use thinset.

I have used both grout and grout caulk in the gap between. I like grout better because I never get an exact match with grout caulk. As long as my gap is similar to my tile grout width it seems to work fine. If my threshold is a dissimilar material (I once had to make an oak threshold) then I use grout caulk to allow expansion of the wood.

If you want the threshold flush with the tile but can't figure the thickness of the SLC, then screw down a 2x4 in place of the threshold. Put a slip sheet on the edge of the 2x4 that the SLC will touch. You can simply wrap the 2x4 in plastic, then screw it on place. The plastic will be the slip sheet.

Pour the SLC. Do the Ditra. Tile. Then unscrew the 2x4, the plastic will act as a release to prevent and SLC or thinset from sticking to it.

You're total thickness, SLC-to-slate, will probably be around 1" to 1-1/8" or so. To get the 3/4" threshold even, you'd need to bed it in 1/4" thick to 3/8" thickness of thinset. That'll work. If you need to go thicker, then you can move away from thinset to another setting material, as thinset shrinks a bit when it cures. That's why it's called "thin" set. It's used in "thin" layers, so to speak. There are other bedding materials for thicker applications.

Or you could do two thicknesses of thinset. Do a 1/4" layer. Let it cure. The next day set the threshold.

I'd caulk the seam between the threshold and the tile since they are on different substrates, so to speak. But you could grout it if needed. You might get some cracking, but it shouldn't be significant.

Thanks to the both of you! Thinset it is then, without the SLC underneath.

Hags00, good to know about the color match for caulk and if using dissimilar materials.

Mongoct, thanks for the supportive instructions! Perfect!