The alternative would be very thin wall radiators - if such things exist!.

I have a single panel radiator in smaller space than yours. Total distance
from wall to "outer" edge of rad is 75mm.

That would not eat up much of your 800mm. I have much less width than that,
and still have room to pass.

In my understanding (as a prospective buyer, not an expert), 40mm is not
enough to for a proper installation of underfloor heating.