Here's the deal:
Two-story c. 2000 house in southern Missouri, lower level is a "walk-out basement" (subterranean on 3 sides) and consistently 10 degrees colder then the main level year-round. Single-zone ducted HVAC in a centrally-located basement closet. Thermostat (ecobee) upstairs in the "great room" with high vaulted ceiling, master bedroom has vaulted ceiling as well. Main level floorplan is very open... kitchen, dining, sitting room, great room, master bedroom either fully open or double-door sized archways. Each room upstairs has standard floor registers and in-wall returns. Downstairs rooms have in-ceiling registers with matching in-ceiling returns. Generally these registers and returns are not more than 12ft from each other (upstairs and down). Stairwell to go down is centrally located (almost above the HVAC closet) and fitted with a standard interior door. No zone controls or airflow controls of any kind (aside from ability to close individual registers).
I had the HVAC system replaced last fall, both the indoor part and outdoor part. I don't know much about it but it's a beefier unit than the original.
Over the winter I noticed it was sucking air inside through the wall outlets in the basement (on the walk-out side). This airflow cooled the electrical contacts so much that condensate would form inside the outlets and drip down the walls all day long. It's safe to say the house is not well insulated. I ended up plugging the outlets with baby-proofing plugs and taping over them with painters tape. That stopped the condensate problem, but air still came in around other seals and seams.
Today we had our first 88 degree day, and the HVAC ran maybe a 60% cycle trying to maintain 80 (!!) upstairs. Downstairs peaked at 71 (digital thermometer reading). It's now past sunset and still 82 out, and the HVAC has been running for 30+ minutes. Presently 81 upstairs and 70 down.
Is there ANYTHING I can do to make this system more efficient? Ideally, 75 upstairs and 72 downstairs. If I set the thermostat to 75 it will bring the downstairs into the mid-60s. But I don't care about the downstairs - it's not presently used as a living space. (If that was reversed and I didn't care about the upstairs because I was only downstairs I'd be pretty happy in the cooling season; I'd keep it at 75 down there and that would probably mean 85-88 upstairs.)
Any guidance appreciated!
(Prior to upgrading the HVAC in the fall, we had similar problems with imbalances up and downstairs but that system was not so modern and it had sections of damaged "fins" on the condenser unit so I expected some inefficiency.)