Property owner declares land value and pays tax based on that value. Taxman has checks and balances to make sure that the declared land value isn't egregiously low balled.
The declared land value is made public and anybody can make an offer to buy the land at that value plus a premium. If the offer is accepted, all is good and we have a new declared land value.
If the offer is declined, a new declared land value is set at the offer price. The owner pays an additional tax to reflect the new declared value and a penalty if it is found that the old declared land value was (significantly) below prevailing land values.
The trick is in setting the penalty in such a way that it becomes unappealing to declare less than fair market value. The risk is that declared market value is unduly inflated to protect against the penalty, but the property owners self interest in paying the least amount of taxes should protect against that. Also applying a (small) fudge factor to the acceptable fair market value when the penalty does not apply should help. Markets do move and there is no need to (harshly) penalize normal appreciation and market developments.
That works for property tax, but it doesn't work for land value tax, because the key difference between LVT and property tax is the former is based on the unimproved value of the property, while the latter is based on the value of the property as it is, with all improvements.
A self-declared value that is legally tied to an offer to sell at a fixed premium is clearly a self-assessment of the improved value of the property, not the unimproved value that LVT is supposed to be based on.
Two notes:
* If a person's offer is accepted to buy their land, we need to figure out how to agree upon the price of the improvements, too. I could imagine a system of arbitrators being useful here.
* People's natural loss-aversion would be a problem here-- one would expect a person to overstate the worth of their land by 50% or so.
I agree that there are a lot of confounding variables, but with the right amount of filtering and smoothing, one can still get reasonable answers.