Just thought I'd post an update as I'm working through this project. I ended up buying a 14ft uhaul truck for $650. Had to drive to Boise to get it, but the box is almost perfect to set on top of the M353 trailer chassis. I decided to go with a little bit smaller box than I was originally planning because I don't want to be too limited on where I can take the truck and trailer.
The overall height of the uhaul box is going to be within 1" of where it's at on the stock truck, and that's sitting on 11R20's. I'm going to have to remove part of the cab-over section of the box (to make sure that I have enough clearance between the M109 box and the uhaul box), but that's no big deal.
This is what I'm working on right now. Adding 2x2" crossmembers that run front-to-back to support the floor of the box, which is made up of sections that run side-to-side. I'm pretty much ready to make the swap, and now it's just a matter of lining-up a lift to get it up high enough to get the trailer under.
Thanks again for helping me choose a trailer chassis. This M353 is EXACTLY what I was looking for.