This ^^^
Just try a thinner set, or moving them over a slot, and see how it goes.
I bought a Ibanez Talman 30 when they were silly cheap to try a set of piccolo bass strings on, EADG but an octave higher so guitar register and gauge, I didn't have to change the nut and it's fine. The tension keeps the strings in the bottom of the oversized 'U' shape, you'd have to play really hard to move the string across and up the slot.