I think your bid is high also. We live in N VA also and last week asked 5 contractors to give 3 bids each: good/better/best. The good bids were Trane and Goodman = $5000 Better bids were Carrier and Bryant = $6000 - 8000 Recommend you get more bids.

The thermostat reads the temperature only where it is located and starts and stops the machine accordingly. Always think of HVAC not as creating a cool environment, but as removing (or moving) heat. Think bilge pump. It is removing heat from an area via the air return and then the air handler either removes heat from that air or in winter adds heat to it (either via heat strip or heat pump) Consider, your heat pump in the winter is removing heat from the outside winter air and adding heat to the inside air via the air handler. THIS IS more efficient than an electric heat strip in the air handler. One zone (system and thermostat) to control the entire three story environment is going to be unstable and varied. Just the way it is. I read about opening the ducts in basement in winter and closing the uppers. that may help. Closing the ducts in basement in Summer and opening in attic may also help BUT, remember, it is about moving heat from inside to the outside. Bilge pump that heat overboard. If you have more heat entering than you can pump, you will lose the ship. Also, you should be removing the heat (air handler return) from the top. You want to remove the heat from the top of the structure. Even a window shaker in the upper rooms would assist in pumping that heat outside, thus causing your central AC to run less. Ideally, cost not being an issue, you would have separate systems for the main floor and upstairs each with its own thermostat. The basement would get the overflow. Where do you live, how many sq feet per floor and average ceiling height on each level? Where is the thermostat located? Stay Cool.... like Fonzie!

I know nothing about why your home is not set up for central air. I can speak knowledgeably about split a/c units. We installed them when we lived in Thailand. They are remarkable, in that they usually feature a dehumidify setting, to get the moisture out without making it too cold, as well as a cooling setting. If they worked at 17 degrees from the equator during monsoon season and hot dry season they ought to work well in Washington state. We went with small units in each bedroom, so that we were only cooling the area we were in, and one larger 20kbtu unit for the entire downstairs.

This is very specialized stuff, but all worked out. If you want to go ahead with this, you need to find a board that devoted to earth tubes or that in combination with other fringe green tech. Don’t get me wrong, it is a fine idea where it works. I don’t think it will work for you. Take a look at the base facts. How much air at ground temp do you need to move to move the Btu necessary to cool the structure? If you do that calculation, I think you will find that you are planning on living in a wind tunnel. For one thing, that will be unpleasant. Second, by the time you move that much air (giant blowers) and dehumidify, you can do a little cooling and (especially) dehumidification with a mini split. If you have a well sealed and insulated structure, your energy and equipment costs will be very low and it does not even make that much difference how you cool it. I thnk by the time you pay to tunnel or invest your own sweat, you can have mechanical cooling installed twice over even if you pay rats with cheese to tunnel. (They work cheap and you could probably train them.)