Thanks, then protection for the floors it is.
In the meantime I put the chains on to play around in the free muck I had delivered while trying to build up a drop off on my property. Some nice dirt, some clay muck. I was moving it yesterday with turf tires and had to break out a shovel to knock down a pile of the stuff that accumulated behind my front tires while I was trying to back up a hill. Could not go forward as it was a cliff. Locking the diff and using the bucket to assist did not work.
Today with the chains on the rear it worked 100% better. Never needed the bucket and only had to lock the diff a couple of times. The only thing is I need to add about 1/2" spacers so I can use a blade or grading box with the chains, otherwise the chains scalp the 3pt hitches brackets a bit.