Narrowest Tires For Some Float On Gravel?

Swapped out my 55mm Mutano Raptors for a 1.25" cross tire in
front and a 1.25" slick in the back for commuting.

Now I've become a little addicted to the livelier feeling of the
narrower tires.

Only fly in the ointment is deep loose gravel - say 25-40mm size.

The Mutanos float over that stuff no problem.

The 1.25s dig in and hunt.

In the interest of avoiding an unnecessary fact plant - and not
spending a bundle trying different sizes... does anybody have a
feel for the narrowest tire that wouldn't dig in to that stuff?
--
PeteCresswell