...Conway Bob, How do I support the floor from underneath by the door effectively without welding a new support?
I'm sorry, I'm not familar with a Burro's Frame and fortunately have not had to mess with my frame. Flooring yes, framing no.
I would expect there are crossmembers in the frame that you can run a stringer in between. And I'd say in general, to do it right, you use the same materal that's in the frame. meaning welding some angle iron between two crossmembers.
Your only alternative is wood, & using wood bracing in that area is providing a weak spot that would or could fail. It's obvious that the first two steps inside that door is the most Hi-traffic spot in the trailer and needs strong support. Unfortunately your support is on the underside of the trailer...where all that yucky, rain, sleet, and mud is at. Unless you dip that wood brace in tar, eventually it'll rot, and you'll only have to fix it again. Adding iron is the lightest, strongest, and longest-lasting choice.
The length of your brace also plays a part. Where are your nearest crossmembers? Or would you be running your brace across the trailer, from doorsill to centerline, or all the way over to the streetside sill. Your shortest run is always the strongest.
Compare strengths...2" angle iron beats a 2"x4" all day long.
I'm sorry Pam, I'd invite a welder to lay in some iron before I'd use lumber. And weld, not attach with bolts & nuts. You drill holes in your frame, and you'll eventually get a crack or corrosion, plus nuts & bolts come loose faster than any good weld I've ever seen.
Are you sorry you asked? <_<