So does anyone have experience with these systems and can I use it to stabilize the temperature without breaking the bank? I know they are pretty efficient but I don't want it to be so expensive to operate that I can't use it often enough to be worth the expense.
They're definitely going to be your cheapest running cost for cooling. For heat they're generally cheaper than everything but wood and natural gas. Though that can vary a bit depending on local energy prices. So it's among the cheapest options. Whether that's cheap enough depends on the building..........................
I'm running two cheap 12K 15 SEER inverter units in my 1,400 SF house for primary heat and air. Place was built in the early '50's so no insulation in the walls and crap insulation in the attic. But the place is pretty tight. T&G everything including the roof deck. North Miss so summers probably hotter/longer/humider and winters shorter/milder than yours. IIRC you're somewhere in VA?
Anyways best as I can figure last summer cooling used 2,000 kWh and this winter heat was 2,100 kWh plus about 50 gallons of propane for backup heat. That's under $500 for the year at my local energy prices
Secondly is there a better solution?
First off it sounds like you've got a serious air leakage problem since everything is getting wet when the temp swings. Do what you can to seal up the building or you're going to be fighting humidity leaking in and energy/money leaking out.
Second insulate the downstairs if you can do it for reasonable money and time. My place I will insulate the attic once I get done with rewiring. The walls maybe, at some point, because it'd require ripping the siding off. And I'd likely never see a return on investment from insulating the walls. If I do it it'll be to kick the mean radiant temperature up in the winter.
Once you get as much of the above done as you reasonably can then start looking at climate control. Based on your description of the shop a minisplit downstairs and keeping the window shaker upstairs would be a good starting point.
And if you do go with mini splits consider tooling up to install them yourself. You can buy everything for what a lot of HVAC pros charge for one install. And some of it crosses over to automotive A/C so you can get more use out of it.