Hilux 40mm body lift tyres

[slo_mo]

Hi,

Just got a Hilux with a 40mm bodylift on it.
Currently it has 33 x 12.5s on it and they look to have seen better days.

They have been gouged out and make the truck wobble like jelly at 80km/h
What would be a good size tyre (with no rubbing) and still be capable to get a bit muddy and take on the road without losing to much grunt.
I will be mainly on the road with my driving so they need to be able to stand tarmac but need to take on mud without changing tyres.

I was thinking either 31 x10.5 or a 32 x 11.5?

Any thoughts