I was assuming the 2x4's were standing on the narrow part so they could possible topple sideways. If they are going to lay flat I would say 1/4 inch ply is more than enough. If you want the 1/2 inch extra lift you could box the 2x4's top and bottom with the 1/4 inch ply to make it more rigid when adding or removing .
You can also probably go with 2x3's and 1 top coat of 1/2 inch ply if they are going to be laying flat. I went with the 1/2 inch in this suggestion in case the camper walls are thicker than the 2x3. In that case the extra thickness of the 1/2 inch would better spread the load.
Depending on wall thickness can you get by with 2x2's instead?
The more I look at it the more I think I'm just going to attach 2x4s at the perimeter of the camper and at the basement walls. I'll use a few screws on each 2x4 to secure it to the "joists" so I can easily remove them if I need to get at the access panels. I'll need to bridge the three supports at the back of the back of the truck bed with a 2x4 since there isn't a single "wall" there. Keeping them attached to the camper will make loading and unloading easier.
I have simular plans but using 2x6 just for a little bit more of a heft to the frame. I will also have 4 or them running the 10 foot lenght and a few cross braces to make sure there is enough cantalever, as mine is 10 feet long and I want the back suported well also. (I have to lift mine over 3" so I need two layers of 2x wood)
one thing I am doing that you should concider is to put foam board the open space then close it up on the bottom with a sheet of pressure treated plywood or somthing. this will give you some bonus insulation value on the floor of the camper and would other wise just be waisted space
I opened up the panels so I could look around under there. It looks just like the picture I posted other than the picture is reversed (the long part of the L shaped fresh water tank is on the other side when looking from the bottom). The L shaped basement walls may be the most solidly constructed portion of the support. The perimeter walls have venier holding in foam board insulation so I can't tell how thick the wall is above the the base framing.
What concerns me is the fresh water tank. The tank is supported by "seatbelts" with lag screws into the bottom of the floor. There is 3/4" foam board between the bottom of the tank and the access panel. The foam board has witness marks/indentation from being compressed between the tank and access panel/truck bed. Most of the indentation is on the long L section with not much on the short L side. I can stand on the foam board without leaving an indentation from my shoe so there is probably a fair amount of load being transmitted through the foam to the truck bed when bouncing along with a full tank.
If I decide to go with 2x4s I'll probably go with 5 going crosswise (one at each lateral support plus one at the back) plus an additional one between the two straps in the picture to support the water tank in that area. I'd use 2x4 blocks between them to support the perimeter and basement walls.
I'm still considering doing a 3 piece platform but using 3/4" plywood on the top because of what I saw at the water tank. The challenge would be keeping them light enough for my wife and I to easily load and locking them in place without making it an ordeal every time I load and unload the camper.
ya I forgot bigfoot put access to everything from the bottom, on some of their models. I am trying to remember now if ti is the same on their newer models but I don't recall seeing any access hols in the bottom halfs when I did my tour, so I don't know. what you could do is build a frame that mimics the bottom so you would have the access points in the fram you build then attach it to the bottom of the camper. that way it goes on and off with the camer, it lets you add a bit more insulation , adds one more layer of defence for water intrusion through thoes bottom panels, but you still can access all the points you need to.
