Wow. I think the simplest response is this. The system you're talking about (or at least the parts of it that could actually work) would probably cost more than your house. When talking about energy saving modifications to building systems, one of the most important calculations is the Return On Investment (ROI), or payback period: how long will it take for the energy cost savings to pay for the initial cost of the system.
Well, a solar water tank is an easy install: there's no need to hook up gas utility to it, and you basically run flexible stainless steel piping out a conduit in the back wall and up to the roof in another conduit. The entire system costs
about $2500 for a 300L tank,
$3300 for a 400L tank, plus
some tubing that runs $3 a foot and a. The government gives about 50% back on this, but then taxes that as income, so about 30%, making this $1750-$2000 to install.
Further, Maryland will grant 1SREC per 1MWh power generated by water heating up to 5MWh; 3MWh is typical for a 150L tank, so I'd exceed the cap. Utilities that burn fossil fuels must pay $400 per MWh generated or supply a credit; these SREC sell on the open market for about $200 at the moment, so for the next 2-3 years at least (i.e. until the penalty is lowered from $400) I can generate $1000 per year in taxable income, about $700/year, offsetting the cost of the solar water system. For just water heating, the tank size of 150L would really pay for itself entirely in 1 year; the system I want to build has to generate space heating in the winter, so 2 years.
A hydronic heater costs about as much as any other heater, although it's got a longer life. It's easy to hook up--no gas hookup, just water piping and attach to the HVAC, which is work I can do myself. It runs a pump and thermostat on regular utility electric. Mind you the furnace I have is from 1992 and shows visible signs of age, so requires replacement. That makes this a non-cost.
The only additional cost is the cost to hook up a secondary gas furnace as a back-up on the water tank, which again costs as much as any other gas furnace. This furnace will usually never run, anyway. I can put the furnace in place myself, but a certified technician must do the gas hook-up. This will be around $2000 total cost (the furnace itself would run $1000-$1500, installation will run under an hour of labor... although I have a cousin who works for the local gas/electric utility and can do both main electrical box wiring and gas utility/appliance hookup).
There is no AC compressor currently, so I'd have to buy that anyway. A natural gas driven AC has very few moving parts (it's an absorption heater, there's no compressor; there's fire and a thermostat, no pumps or anything) and to my understanding they're generally inexpensive. It just needs a natural gas hookup--again, labor that I'd have to outsource; I'm not hooking gas appliances up by myself, that's insanity.
You really think this is going to cost more than my house? It looks to me like the only additional cost is a secondary gas furnace for a water tank backup. Overall the total cost would come to some $6500 for the units ($2000 water heater, $1250 for each of 2 furnaces, and $2000 3 ton natural gas AC unit--you think I need 3 ton? They just come that big!); but to install a normal furnace, AC, and water heater would come to the same, and I need at least two. The water heater I can probably avoid, but the ROI on the solar water heater will be extremely fast.