The mini-split route idea is a great solution, but I am wondering if you have an unvented or poorly insulated attic that is a contributing factor to your problem. If your attic space isn't setup properly and you throw a mini-split at the problem, it is sort of like pumping water out of a boat without fixing the leak that is flooding the boat. Even something as "simple" as a powered attic vent could help in HVAC performance and operating costs. If the hot air can't vent or your insulation is inadequate, it just stacks down and heats the top floor.
Unfortunately, I don't live in a free-standing house. It's a townhouse, so it's connected to other units so I don't think that I can make changes to the attic.
The other thing I would be looking at is if the HVAC run up to the second floor is done properly or if the dampers are not right. A house that size really shouldn't have much trouble if everything is balanced right.
I don't seem to have any dampers at all as far as I can tell.
Having the nest with a second temp sensor would just force your HVAC to work harder to cool the upstairs.
Yeah, I get that I would be pushing the HVAC system to simply be on more, but at the very least I could actually set the temperature upstairs instead of having it fluctuate so wildly. Often, I'll set the temp low at night to be more comfortable. It'll be to the point where I'm basically freezing with the sun down. But then in the morning, when the sun rises it's unbearably hot.
The single sensor nest can be a smart move to reduce costs with the higher degree of control.
What do you mean by this?
Having dampers installed does more or less the same thing as closing vents, but with a higher cost. A zoned system is expensive and kind of silly on a house of that size.
So there's no real reason to get dampers installed then?