You pay federal taxes, so do what's within the law. In my state, it's both lawful and common to set up and leave a tree stand or blind on forest service land for months at a time. Technically, that's "claiming" a spot just like setting up a tent. None of us care. If the tent, stand, or blind is empty...I still hunt the area. That's completely norm for most people I know hunting public grounds. If it's occupied...I just go hunt another area. We can all share the woods and respect each other's property without being petty.
Lastly, nobody should be setting up a blind, stand, or tent on public land with the notion that the area is now closed off to every other tax payer. Just because you put a tent up doesn't mean a hunter won't hunt the area. So don't feel bad about setting up early, as most hunters won't feel bad about hunting the area if you are nowhere to be found.
I would set up trail cams on your gear though. A lot of folks don't abide by the, "do what's right..even when nobody is looking."