I took a look at the Skutt website, and that doesn't appear to be foam.
It is an insulating fiber insert, designed to keep more even firings by better insulating the bottom. Your lid is also fiber insulation, same idea, keep more heat in and even out the firings. So check it out, and if it isn't foam, leave it in. I would put shelves down on those posts and I would also contact Skutt to see if they can offer more advice on the loading than is available in the manual, or the brief intro from your installers. 1-503-774-6000 That is an expensive bit of equipment and doing the most you can to treat it right is in order I'm sure you will agree. Skutt support is supposed to be top shelf.