Levelling and raising a sloped floor

I am just about to completely rebuild our utility room (aside from the boiler it is gutted back to bare plaster). Currently it has a concrete solid slab finished in what looks like a quarry tile. The tiles are pretty even and well fixed. The room is about 2.2 x 3.2m, and the floor slopes about 20mm downhill across the narrow axis.

I want to raise the level, as currently there is a step down of approx

Since I have plenty[1] of spare PIR insulation boards to hand it would seem daft not to also take advantage of those and make an insulated floor while I am at it.

Initially I thought about sticking down a DPM (lapped up the walls) then a layer of 60mm + 25mm PIR, and then screeding over. However that would mean the screed at the "thin" edge would only be about 40mm deep. Which would suggest needing to use a fibre reinforced concrete. Also it would need a fair amount of curing time.

Then I though of using something like Hardiebaker board - a couple of layers of 12mm laid in opposite directions and bonded with PU adhesive would make a very strong floating floor on top of the insulation. Finish it with some fibre reinforced SLC and it would be good to use in a few hours. Only problem is the slope - it would need a massive depth of SLC at the "deeper" end of the room.

So further options - build up extra layers of hardibacker (can get 6mm as well as 12mm) at the deeper end, and let the SLC remove the "steps".

Or possibly, and my current favourite, cut 0 - 20mm firring strips out of treater timber, pu them in place on top of the DPM at 300mm centres, then glue some 12mm OSB3 on top. That gets rid of the slope. Add 85mm PIR layup on that, then 24mm Hardibacker, and SLC to finish.

Any other options you can think of?

(The floor needs to be decently strong, feel solid, and be able to cope with a washing machine bouncing about on it. Final finish will be glued down LVT planks)