Is your area equally divided between the floors? Your symptoms are frequently the result of short comings of the duct system (poor design, poor intallation, etc.). If your duct runs leading off of your main trunks contain dampers, you might be able to lessen the problem by adjusting (not shutting off completely) them seasonally, so that you get more cool upstairs in the summer; more heat downstairs in winter. If your equipment is oversized, it will not run long enough to properly heat or cool the areas most distant from the furnace/air handler. Listing model numbers of equipement (furnace/air handler, outdoor unit, coil, is used, would be helpful. Also your location. V

Or, you could T it in and see what happens. It might be just fine, what have you got to lose? A few hours of work and a few bucks' worth of sheetmetal. I'm sure a professional could come up with a multi-thousand dollar solution. In fact, call a couple of them out and see what they say. Should be interesting. "Never ask a barber if you need a haircut..."

The answer here is the obvious one: You need to insulate and install storm windows. Do that before you consider any equipment - otherwise it will all be sized incorrectly. There are ways to insulate the house. Cellulose can be blown in from the inside or the outside. Closed Cell Foam can also be injected the same way. Cellulose can be blown into the attic and the crawl space walls/rim joists can be sprayed with foam also.

Before you spend all that money, have you looked into properly insulating it? What kind of insulation do you have in the walls and the ceiling above the room. I have a room like this over my garage and was constantly thinking of adding some specific room solution for it. It ran 25 degrees different in the winter and 20 in the summer from the rest of the house. Adding a new furnace with a vs blower in basement (had an old 60 yr old gas hog) brought me to 10 degrees closer to the rest of my house. After alot more research i found that uninsulated kneewalls to be the main problem with these rooms. I cut 3 2.5 inch holes in the kneewall that ran 5.5 X 20 feet and saw I had a mini attic space there about 2 feet wide at bottom and .5 feet at top with No insulation. (imagine a long triangular wedge) That empty space allowed any heat gain from the front slope of the garage to go right to the room negating any ac or heat from the room in winter to just seep out wasting my money. I pumped 5 bags of cellulose last January into this space and then patched the holes. (Ceiling was done b4 new furnace to R50) Immediately i noticed that this room went from minus 15 degrees from the rest of my 2nd floor to within 2 to 3 degrees difference which is tolerable. Im even using the room now in the summer with no diff in temp from the rest of the ac cooled house which i havent ever been able to do before. Total cost to insulate the kneewall was 80 bucks and took me bout 10 min drilling holes 15 mins pumping insulation and 30 mins patching. I painted the patches the next day.