If air conditioning, open when humidity is low and close when humidity is high.

Klem, I am a control freak by nature and these kinds of systems I worked on what seem like a life time ago when I was working in facilities maintenance for what is now mostly a defunct cell phone manufacturer. Realize this system does not provide the heat to the structure... it is not a boiler type system. It is your hot water system on steroids. You already have the hot water that is in the hot water tank. The pump is merely a way to circulate it. The pump would come via commercial type application. The thermostat is merely to turn the pump on or off via a predetermined set point. Bell & Gossett are a well known brand some 20 years ago for this kind of application. As far as power problems go, the best way to alleviate those concerns would be to install a generator that would kick on to run your furnace, power the water heater and the pump and controls of the system. You could size the generator as big or as small as you want depending on what your goals are.

I suspect that the vent screens were placed first, simply for ventilation, and then they were tempting/convenient access points over the years to bring in gas/electrical with the least amount of work. It looks to me like the large holes, like the one where the gas line enters, were simply sloppy work when the line was put through, rather than the work of a rat. There is nothing wrong with having these services come through wire screens like this, but it will be a lot of work to get these off, replace them, and have it all repaired and looking neat. For example, how would you intend to deal with the gas line that goes through the center of the screen, meaning...how would you get a new, intact piece of screen on without undoing the gas pipes? Here is my suggestion: leave the screens in place and buy some matching wire to make neat patches. You can simply cut the patching pieces so that there are stubs of wire around the edges, and then these can be bent over the existing wire with a flat blade screwdriver and/or some needle nose pliers to hold them in place. If you don't like the idea of small patches, get pieces of wire mesh that are as large as the entire openings and then fix them in place over the wire in the existing openings. When you're finished patching, get some Rustoleum brand spray paint to make everything blend in and to deal with the existing rust.

How much noise should we expect from a HPWH? - About as much as a fridge What downsides, if any would we experience with a HPWH vented to the conditioned crawlspace? This can work - but know that the air going into the crawl space has to return back to the water heater on the main floor. You have to provide some way for that to happen (a vent, openings, etc) One reason I was initially attracted to a HPWH in the pantry is the cooler/dryer conditions that would result in that space. is that a foolhardy approach? No, it's not. It's fine. Again that air being sent to the crawl space has to circulate back to the water heater. It will cool and dehumidify that area. Also a slightly unrelated question: we have to other hot water "zones" which are ~ 23 ft from the proposed water heater location. Is there a general rule of thumb regarding distance from the heater where electric demand water heater becomes preferred? The answer is complicated. What is the fixture being served, how sensitive is the use to delay in getting hot water? Also, plumbing layout and design matters. So, for example, let's say that one of the uses is the master bath sink. You use the bathroom and wash your hands - you will notice a delay. The fixture will use 1.5 gpm - if you use home run system and use smaller pipe, you will get hot water much faster than if you use a branch system with 3/4" lines. Insulating hot water lines keeps the water warmer between uses also. On the other hand a bath tub, for example, probably doesn't matter. It's moving a lot of water (4 or more GPM) and nobody really cares if it takes a few seconds to get there.