Quarter the model to take advantage of symmetry. The symmetric fixtures will partially restrain the heel guard, which is handy.
Start with a bonded contact for everything to make sure you can mesh and run the model. The mesh will have to be pretty fine to mesh that detailed geometry.
I believe a virtual wall could stand in for the contacts along the edge. It should be less computationally intensive than a proper no penetration contact.
My personal preference is to restrain something like this as close to reality as possible. I would use roller-slider on the underside (only where the grate is supported). I would then restrain a couple orthogonal edges along one one side (one for X and one for Z). I trust you have already split the surface on top and applied either a pressure or total force load. Don't forget to add gravity.
This one is pretty simple and straightforward.
That result actually looks pretty cool!
I think the model is just weak in that direction. Those little bars are much smaller than the I-beams.
However: this study probably just isn't realistic enough. For one the loading condition is spreading equal loads onto each of the mid-sized beams. In reality, with your wood pallet to spread the load, all those would move together. Adding in the wood pallet wouldn't up the computational requirements that much.
The biggest hindrance to realism, though, is probably the lack of membrane stresses due to the nonlinear behavior of the structure. Try this as a nonlinear problem with no-penetration constraints in place of the virtual walls. (Well, first try it as nonlinear with fixed boundaries, then with sliding boundaries, then with no-pen).
Hopefully your static study is solving relatively quickly.... if not see if you can get the mesh coarser before you step up to nonlinear.
Define 'excessive', what are you getting for values? You may be over constraining and making the system artificially stiff. Do your resultant values make sense?