I don't think that Georgists have the misunderstanding that you claim. I'm not a Georgist, but I do like many of their ideas and listen to some modern day ones.
What you are arguing against, the idea of taxing something based on its "value" where everybody already values things differently, this is not a new thing. It's not hard to implement. We already do it. It's here in the real world. We have property taxes. Each property is unique, non-fungible, everybody has different valuations for every property, and yet somehow we still work out a "market" value.
Establishing land values is only a slight modification of establishing property values. It's easily solvable, and the places that have implemented it have not had difficulty establishing the valuations for tax purposes, by basing these valuations off of market transactions.
But, you might argue, what if your personal valuations are different than what the "market" values them at? Well good for you, because then you are likely able to find a great deal more value out of a property than what the market values something at.
And maybe if the market values something far less than what you value something, then you can hold on to it for cheap! And if the market values something far more than you value something, you can avoid the expense of buying it, or if you have it, you can profit from selling it.
If markets are useful for something, it's finding out what a population thinks something is worth. When it comes to land, and who is excluded from using this precious and finite resource, and who is allowed to use it, market valuations are extremely useful. We can watch transactions to figure out who is using up the most of what other people want (i.e. holding land with high market value). If somebody is hoarding a precious resource, but unwilling to pay the taxes to hold onto it, perhaps they don't actually value that resource so much after all.