> assumes the usual economic myths of a fixed amount of money
Not at all. Henry George's original ideas included defining money as essentially an IOU pointing to an underlying wealth; and wealth can indeed be increased.
> The problem with land is not rent, it is the power of exclusion, which leads to hoarding
This sentence makes me suspect you've confused the antecedent of LVT with its result.
Fixing hoarding is The Point of LVT.
You're misunderstanding the term "rent", which unfortunately refers to both the common "I charge you X money on a recurring basis in exchange for occupation" and the more precise economic rent[1]. LVT would disincentivize economic rent, which would kill speculation and encourage more productive use of land overall, which would decrease exclusion and force hoarders to sell off their holdings.
[0]:https://astralcodexten.substack.com/p/your-book-review-progr...