I would say running the main unit is of course the best outcome because you are circulating the entire volume of the house, BUT you will be using the most power. The amount of heat given off by the dehumidifier might cause your GT unit to run a minute more during cycles. But you are right they run a lot of watts over a long period of time.
Options I think might help would be a heat pump hot water heater. Sadly this is only going to help as much as the hot water you use, and the house being empty means its not going to run that much.
You could build a small mini split, 5,000 btu window unit with the condenser outside. This would solve the added heat problem with the dehumidifier. Also running R290 would save you some watts.
Or you could drill you a bore hole and do a DX Geothermal unit. I would guess you could get a fairly high EER value from that.
If building a system is not a option for you, how about one of those small portable AC units. I know the higher end models have a dehumidifier setting and they vent the hot air outside.
Amazon.com - Honeywell MN12CES 12, 000 BTU Portable Air Conditioner with Remote Control - Black/Silver - Bucketless Standing Ac Units
Just some ideas. Good luck and death to humidity!
