I'd lay down plywood over the
entire floor area - wall to wall - no gaps.
Thinking 1/4" would do the trick - but the thicker you go the better protection and wear and tear you get.
I have had 1/4" plywood on the floor of my landscape trailer (over the old 1" x 6''s) for about 2 years now and it has lasted pretty good --- and it stays outside too.
