I have a brand new Carrier Infinity system - variable speed compressor, fan, smart controller with app (basically an ecobee4 built for Carrier) etc., and am still working to try to balance it.
My office is upstairs in a BR on the opposing end of the house from the evaporator. I have a fair amount of gear in it, so it's the warmest room in the house.
So far I have cut in another return vent in my office as suggested by the HVAC guy. The single return in the 2nd floor is in the hall on the other side of my office so that was 2 minutes with a multitool and covering it with a vent. That helped, but not as much as I had hoped. More return vents are better, but not an option for me.
While I have some registers closed off (living room, bathroom), we have new wood floors in the main level everywhere else with fancy wood registers that can't be closed and a toe kick register in the kitchen island that also can't be closed off.
Next step is to install dampers in the feed to each of those rooms and start closing them off. Since I have an unfinished basement, this is easy to do. You can hang meat on the main floor and the floor is ice cold, but it's 6-10 degrees warmer in my office by early afternoon. I'd rather close the ducts off near the source than cool off all that ductwork and close at the vent. Perhaps it serves the same purpose, but I can't close them anyway so that's my option.
I've also been running the attic fan when I feel it getting too warm in my office, and that helps pull cool air up from downstairs but my office still runs 3-4 degrees warmer with all the equipment in it.
My advice to MJ would be to see if you can get more return air from the upper levels and close off what you can on the lower. However, nothing you do will beat physics and the fact that cold air sinks and hot air rises.
ETA: One thing I forgot to mention. Make sure your floor registers are free to blow that cool air. If there's furniture in the way, you may be able to use some of the 90* clear plastic magnetic base vent covers to help. Our master has vents near both front windows and our king bed straddles both and covers a good portion of them and installing the vents helped both heating and cooling.