I'm no expert on Georgism but I think there are reasonable answers to your questions.
1. "Coffee shop draws more commence drawing more affluent people pushing up LVT driving out residents faster than even the spectre of “gentrification”"
This is an impossible premise. The relationship between the cost of the LVT and the popularity are directly and inseparably linked. LVT only goes up (and stays higher) when the neighbourhood is popular. It drops (and stays lower) if the neighbourhood falls out of popularity. In real life it would reach an equilibrium, but it might encounter some volatility along the way.
This is overshadowed by many more factors than a small increase in taxes, and I would propose that an LVT is a minor factor in the popularity of neighbourhoods.
2. Similarly how do you think about new uses for land emerging? If I lease desert land for a data center because it’s so perfect for it, instead of buying it … how (and when) does it show up in LTV increases? What if I trade you some other benefit to keep it out of LVT impacting records?
The tricky part about LVT is that it requires an assessment of value prior to realisation. Popular methods include using a combination of average of realised land prices in the area, against a velocity coefficient (the general gain/loss over a period of time), modified by negatively and positively correlated correlates like proximity to public transport and parks. There are countless ways proposed to do just this so I won't retread worn ground.
In the case of the desert data centre, it is likely that the land will not increase much in value. This is by design, because we want data centres (and similar industry) to move into the middle of nowhere so that scarce land is instead used for more productive enterprise like housing for workers so they can get to work easily.
3. Are you just costing the world coordination surplus by forcing high value enterprises to distribute themselves (inefficiently) just far enough apart that they don’t drive up each other’s LVT? That’s a deadweight loss.
This is the brilliant part of Georgism, and the reason I "converted." A well designed LVT imputes the social costs (implied by their economic costs) of the use of land. It then gives the businesses the fully informed choice of how to deploy their capital. It could be that the efficiency you allude to is real, and is worth remaining on high value land. So be it. The business is the best actor to make that decision. On the other hand, if the deadweight loss is lower than the LVT, then the land should be better utilised by another company which would have better utility for its location.
Georgism aligns social costs with business interests in a way no other tax currently does. Meaning that businesses act in their best interests, and in doing so, act in the best interests of society.