I checked one of my ride on mowers for the up and down movement on the front axle and it was 16 mm so if the ground was flat the axle could go up on one side 8 mm.It's not much on this mower. I've just measured where the axle bottoms out, I should have measured the centre of the wheel for the wheel travel .
The 16mm in the pic below was with the other side of the axle pushed up to bottom out the clearance.
I think generally they have at least 20 mm to 50 mm wheel travel.
If you went to quad bike brakes you might get away with using quad bike wheels as there are a few different sized wheels that may match the mower wheels height.