As I said, your plan is marginally better. But it has the same flaw of all redistributive systems:
It punishes efficiency, and rewards waste.
I think you are mistaken. Today to rent farmland costs over $250 an acre. Under this system the farmer that actually does all the farming would see their rents go down. Maybe $100 per acre. Thus, the farmer will receive more profit from farming the land and overall the productivity of the United States farmland rises. It rewards efficiency since land rents don't go to the landowners. The most efficient farmers will win bids.
There is no redistribution, it says land is free like air and owned by the people of the USA. If you use more, you pay more. The current land laws of the United States offers dual ownership, the land is owned by the States and private property. The States get their share in property tax. The reason why States want you to build big houses as they cost more and they can charge higher property tax.
Redistribution:
Economics . the theory, policy, or practice of lessening or reducing inequalities in income through such measures as progressive income taxation and antipoverty programs.
Or, in your case, paying people for using shit land, and punishing them for using valuable land.