There are many ways of capturing land rentCommonly referred to as land tax in the literature and all of them are better than nothing. But an elegant idea deserves an elegant implementation. So let's find one. This is my solution.
Land should be rented from the government using a continuous auction to determine the priceThis is essentially the Harberger tax as discussed in this paper. The winning bidder becomes the land's steward which grants them exclusive use of the land so long as they remain the highest bidder and pay on time. If someone comes along who values the land more highly they can start a bidding war with the current land steward until the new price and steward is determined.
In the case that the winning bidder is someone new then it presents the tricky problem of how to compensate the previous steward for the loss of the improvements they built on the land. My solution is to allow the two parties to negotiate a price between themselves. With the fallback solution being to demolish the improvements at the new stewards expense, though if they use government approved demolition contractors they would be allowed to subtract this cost from subsequent land rent payments. This would prevent hostile takeovers being profitable unless the new steward has a much better use for the land in mind. i.e. people can't profit from stealing the investments of others. This scenario might sound wasteful. But it would only occur when someone has a significantly better use for the land. Existing stewards will tend to value their land more highly than anyone else because the improvements are tailored to their personal requirements and tastes. And if someone values the land highly enough to forgo the use of it's existing improvementsThough the government should take this as a very sincere request to create more land of this type and step in then they must have a much better use for the land in mind and not letting them execute that use would be more wasteful than demolishing the existing improvements.
In the case that a steward of a plot of land wants to sell they would simply lower their rental bid to whatever value they are now willing to pay, $0 is fine, and this would invite a bidding war to determine the new steward.