The only good thing nest has going for it is is their marketing. It over promises and under delivers, just like Apple products. Ecobee is a far superior product with better logging and reliability. The sensi is cheaper and still very reliable and decent looking. Honeywell is had some missteps and was quite complacent, but their commercial products are rock solid. (I never buy their retail stuff. It's made too cheaply.) Nest has helped to move them out of their complacency a bit. They still need more of a push, as they own most of the advanced IP related to controls like thermostats. Nest can only do so much without paying royalties. As for the nest, well it's not very smart at all. It looks nice and that's about where it's innovations end. They keep trying to use power stealing, something that everyone else gave up on a decade ago as it doesn't work with modern heaters, due to the circuit boards in them. Their UI is completely messed up, with important installer settings just missing or hidden in the phone app. I've ripped more brand new nests out and replaced them with other brands due to them not working then I've installed new nests. When used with a common, they work ok, but unless you get a great deal due to a utility rebate, they aren't worth the money. Yes, I'm registered with nestpro.
If you set the temperature on the fireplace, what is there for the neighbour to do? You mean when you want to visit for a weekend, you raise the temp? Part of the reason is lasted this long is that modulating valve, it keeps the flue out of the condensing range. Off and on cycles will allow it to condense, at least momentarily. All heaters work better running continuously.
Now with all that out of the way, like I said before, the most legal way is to buy a new fireplace that has electronic ignition. If your jurisdiction is less restrictive then mine then replacing the valve with a standard, standing pilot, electrically operated gas valve will work. With electronic ignition, you'd have to use a single try, and lockout control. Not something I'm suggesting though, as it's the most dangerous and you don't have a manufacturer to blame if things go really bad.