[billybek]

Getting a good contractor in to have an in person look will go a long way to getting these systems to work as a system.
That ducting I can see in the photo looks to be mostly flex ducting. I can't even imagine the loss of flow due to resistance from this type of ductwork. Plus the fact that they look like they have been flattened and that significantly reduces the flow area and increases resistance to air movement.
If possible, I would have them re run the mains (supply and return) in hard duct that is seam taped ad insulated. Accessible zoned dampering at the trunk or diffuser or both would be a good thing.
The advice of going to a zoned system varying the airflow based on temperature is a good one but may be expensive.
The solar panel install on the sunny side of the roof with an air space under them will reduce the heat load on the upper floors and ceiling space.
There are tons of options out there. A properly installed and set up system will likely pay for itself in reduced energy consumption.
I would not be afraid to look into mini splits that could handle a difficult zone to service from the existing mechanical area.
I was looking at one the other day that the indoor coil looked like a painting frame that the home owner could change to suit the decor.