Can you raise the floor a bit? The thought - leave the slate floor, place 20mm or 30mm of insulation (e.g. high density EPS) - more if you can manage the thickness - less if you can't and put an engineered wood floor over. Take advice from the wood floor manufacturer about intervening membranes. Even an engineered wood floor (1/2" or so thick of the click fit type) on its own will make a surprising difference to the warm feel of the floor.

A wide skirt of insulation laid horizontal just below ground level around the outdoor perimeter of the building - stop the downward-and-outward-back-up-to-cold-surface heat loss from the floor. A shallow french drain under it, to keep the top layers of the subsoil bone dry. Leca can double as the inorganic mineral insulation medium as well as the no-fines aggregate of the french drain. Then leave your old floors undisturbed.

You might also consider VIPs (Vacuum Insulated Panels) e.g. Kingspan Optim-R - would give good insulation for little additional depth, is a little fragile and wouldn't help with breathability. I think costs are about £60/sqm.

The walls of the house act as radiators connected directly to the soil, so heat doesn't need to flow out through the soil outside it can go straight up the wall and away.

With underfloor insulation the walls of the house still act as radiators connected directly to the all-warm slab (or screed) edge above the insulation, from where heat not only flows up but also down and out into the stone-cold surrounding ground. Also heat lost direct from room to wall not only flows up but also down and out.

With outdoor perimeter insulation instead, yes the walls are connected to the edge of the block of floor plus subsoil, which goes from warm to cold with increasing depth, from where heat flows only upward, but not much down and out into surrounding ground because the ground kept warmer under its insulation skirt. Also heat lost direct from room to wall flows only up, not much down and out.

The comparison would need Therm modelling, but I think would be close. Lack of ground floor disturbance remains though.

Slab perim insul is usually quite nominal.
Perhaps what has dawned (on me) is that exterior insul to isolate found wall from cold surrounding ground (pref by vertical downstand where founds are deep, and/or horizontal skirt where founds are shallow) is worthwhile, whether or not slab is insulated and whether or not wall is insulated. On top of its great advantage of not having to disturb the ground floor.

I said

Posted By: fostertomThe comparison would need Therm modelling

i.e. not done (yet) - isn't it OK to throw a useful hunch into the arena?

I always put insulation below the slab and used EPS now graphite EPS, the mass which stores heat is then on the warm side of the insulation, I also put a combined vapour barrier/dpm on the warm side of the insulation.