It's just one of the reasons some people progress to a hard floor.....or hybrid/van.......money permitting !!
Park the wheels on blocks and take some plastic pallets !! Then you have one of the benefits of a hard floor...
That's actually a great idea
with the new wheels my tent's drop is a little bit short so this would help that, just need some rope extension loops on the peg loops, get some lightweight stackable pallets like in the pic and you could easily just throw them on top of the travel cover for transport, it wouldn't add much, if any more time than checking for sticks and rocks laying out a mat and then still having to still wipe the floor after, would be one of the few ways of successfully keeping the floor out of the mud.
I will keep an eye out on gumtree as these are sometimes offloaded for free as well, another Mod to add to the list.