I’m a tiler too.
For a floor stable enough to take slate I’d use Hardie backer 250 (available from B&Q as well as builders merchants). This is glued to the floorboards with FLEXIBLE floor tile adhesive then screwed also. You can then use a flexible rapid set adhesive to stick the tiles down.
Ditramat is fine for use on top of floorboards and plywood but they must be SCREWED down at every joist and be in good condition. Nailing ply down isn’t enough, you could however screw ply over the top of floorboards and use a specific adhesive but the ply needs to be 18mm and screwed at 150mm centres to do any good which leads to the floor height being too great in most circumstances.
Whichever method you use the costs are about the same and the adhesive quantities are about the same, I prefer the Hardie backer as I find the more rigid you can get the floor beforehand the better when it comes to tiling, especially with large format tiles.
Don’t forget to clean and seal the slate with something like HG slate seal or Stain Stop before laying and grouting as this helps you wash adhesive and grout off the surface.