Hey man, I just went through this whole deal last year. Here is what I came up with:
*The raft floor doesn't support any weight or weigh that much itself- you don't need cross members.
*Do continuous 2"x12" centered under the tubes instead. The trailer sides act as one support underneath the 2x12, but you may need an additional support on the inside of the trailer due to the width of your trailer + raft (my trailer sides were close to the center of the tubes so the 2x12 are resting only on the trailer sides + the wall of the trailer).
*Use treated 2x12 and no carpet. Carpet will just hold in the moisture and speed up the rot.
*Once inflated, my floor is up above the bottom of the tubes and I can fit all my gear + even large coolers underneath the raft, in the trailer. You can balance the load and raft a lot easier this way. With a roller I can easily slide my raft back a couple feet to access gear for camping the night before at the put in.
*Consider making a roller. I didn't build one at first, but after a couple times trying to hoist the boat up at the takeout made me realize why I wanted one. I made mine removable so I can still use my trailer as a utility trailer.
*Also consider adding a winch. With a roller + winch you can be off the water from a weekend trip in a few minutes. It's great.
For my roller, I used flange bearings from Ace Hardware that fit in the ends of 1-1/4" galvanized pipe and have an inner diameter that fits 1/2" steel rod. Here is where I got my inspiration: Trailer Roller - Wooden Boat People
If I was gonna do the roller again I'd use 'roll-end bearings' or 'sleeve bearings.' They come in a variety of plastics and are not susceptible to water damage like my bearings, and you can get them made to fit in standard sizes of the larger diameter pipe that is less likely to bend (1" or 2")
Sleeve Bearing @ McMaster-Carr
Trailer Roller Bearing @ DriftBoatParts
Hope this helps...