Ford raised the cab height with the first Superduty in 1999. I discovered this the same way, bought the (1998 Bigfoot 9.6) camper originally for a Dodge 2500HD but had to raise it 2" in the new 1999 F350 that replaced it. The Bigfoot design concentrates the weight around the perimeter and over just a couple of crossing bulkheads. You can usually see where they are by the location of the access panels and the scuffing on the bottom. I would put some harder members there, and fill the rest with foam. I made a full sized platform from 2x2 fir and ply both sides - worked fine but was very heavy to install and remove. If you are going to take the camper off much you want the platform in pieces you can carry. An alternative I though of too late to implement (don't have that camper anymore) is to attach the platform to the camper, it comes out with the camper.
A year or so after the Superduty came out, Bigfoot changed the molds to add a few more inches under the cabover. My 2008 Bigfoot fits fine without any spacer.