Looking for some HVAC suggestions to better cool my stifling second floor

Hi all. I have a 2 storey, ~1200 sq ft home in a hot climate. I have a single HVAC unit...central air and ductwork, electric AC/heat. There is no zoning to the system. The thermostat is downstairs.

Everything is great in the winter months. But in the summer months, the upstairs is absolutely stifling. I don't have a thermostat upstairs, but it feels like it stays at least 10 degrees hotter than downstairs. I get that hot air rises, but considering the bedrooms are upstairs, it makes things unbearable.

My HVAC air handler and condenser are from 2008, so they are rather old and I'm likely to have to replace them soon. When I do so, I want to figure out how to keep the upstairs more comfortable.

Before I start asking companies for quotes, I want to figure out what I'm doing first. Some things I've come across...

1. Install something like a Nest system with a remote temperature sensor. Place the temperature sensor upstairs and have the Nest use that to figure out when to cycle the AC on instead of the downstairs thermostat. I could install something like this myself instead of needing an HVAC company, though it isn't necessary very efficient.

2. Consult with an HVAC company about having dampers/a zoning system installed. From what I've read online, it seems like people are saying this isn't really financially worth it. But if I'm at the point where I want a new system anyway, would it make sense?

3. Window AC units are an obvious "solution", but I can't have them due to the HOA.

4. I have read of suggestions of people saying to close the vents downstairs in the summer, but it seems like this is bad advice, as supposedly it will stress your HVAC and cause it to fail prematurely.

Edit: Just found a new one...setting the fan on the thermostat to "on" instead of "auto". Although some people seem to warn of mold growth.

Would love to hear any and all suggestions. Thanks!