Firstly, how do you deal with people who assert that "the state owns everything already" by pointing to eminent domain and whatnot? It's a very frustrating and dishonest argument, since it's obvious what I mean, but I'm not sure how best to articulate the distinction.

Secondly, people run back and forth between a concern for improvements being lost due to unaffordable land value taxes (ergo disincentive to improve) and land being valued according to their improvements and then taxed as such (ergo further disincentive to improve).

Even if you were to entirely expropriate the task of assessing land value to the state or other third-party (which I'm reluctant to do), that doesn't stop people from valuing land differently by it's improvements. This is the biggest issue I have with Georgism to date, it's only rational to value land more highly after it's been improved (and I recognize some improvements may even be considered to be a cost; I gotta bulldoze a house already there), but how do you prevent that from informing the tax? Or how does it inform the tax without disincentivizing improvements? I've asked this a few times and I've not been satisfied with the answers I got.