You got my creative juices flowing, well not really creative since I just replicated your layout using my cabinet software and used blind dadoes so you still have a clean front edge that we could even edgeband if wanted. For the wood I would probably use 9-ply baltic birch (not stuff you can get at Home Depot). The baltic birch is incredibly strong and lighter weight than some other materials. It's also typically very flat which makes for a strong and square cabinet.
I just threw this together and would probably change the dado depth and width and I would also add dadoes into the back panel for added strength. This would be one heck of a strong cabinet. If your interested let me know and we could work out the lid and hinges, I just need to know how you want it to open up.
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DD F250 SC V10
Something new this way comes, something else Fordish for the trails, just not sure what yet.