How to improve HVAC system to make upstairs rooms more comfortable

My home was built in 1985 in the US with conventional HVAC design of that time. Wooden frame house. It has central air conditioning (ducted) and we upgraded to a natural gas furnace recently. We experience both hot and cold temperature extremes in summer and winter, as cold as 0 Fahrenheit and as hot as 102 F.

One of our major problems is that the temperature on the ground floor is often much cooler in the summer and much warmer in the winter than in the upstairs bedrooms. We don’t inhabit the basement ordinarily so the temperature down there doesn’t really matter.

So, if we set the thermostat to 72 Fahrenheit on a hot summer day, an upstairs room will be around 80 with the door open or 85 with the door closed. The living room on the ground floor will be right around 72.

In winter, if the thermostat is set to 70, the ground floor will be 70 but upstairs might be 66 in a room with the door open, or 62 or lower in a room with the door closed.

The longer the door is closed, the worse the temperature difference becomes in the upstairs rooms.

Better insulation could delay the problem, I think, by keeping the heat out in summer and keeping the heat in in winter. However, what ultimately ends up being necessary is to have per room temperature control. With a central blower just blowing the conditioned air equally through all the house’s ducts, this doesn’t seem possible with the current system.

What sort of upgrade should I make that is a balance between affordability and practicality? My end goal is to make occupants in upstairs rooms more comfortable even if they close the door for long periods of time (e.g. while sleeping or talking on VoIP and not wanting to disturb others).

In the winter, an electric space heater is reasonably economical and extremely easy to install (just unbox the thing and plug it in). But removing heat from a room isn’t so easy in summer, when the hallway upstairs is already 80 F or hotter and the outside is 90 or above.

Also consider that the upstairs occupants use plenty of electronics that generates heat – in one room I am dissipating about 750 to 1000 W regularly between a gaming desktop, monitor and several peripherals (router, many wall warts and USB devices, etc.) This extra heat helps in the winter, but increases the desired amount of AC needed to keep the room cool in summer.

Is it possible to upgrade the centralized system where each room can be heated or cooled individually without having to install a space heater and a window mounted A/C unit for each upstairs room? Ideally with a thermostat for each room? What would such a project entail? I’m assuming some significant ductwork would be needed, and a significant HVAC system upgrade?

To do this properly, would I need to have any qualified electricians or HVAC or building code folks get involved at some point, or could I totally DIY it with the right tools and help?

Edit with additional information:

• All vent registers in the house are 4" x 10".
• Return register size is about 3x the total area of the output registers and there is one return register per floor. Upstairs return register is near the ceiling, on the wall in the hallway. The hallway is usually the best-calibrated to the set thermostat temperature, probably because there's a huge open airway — the staircase — equalizing the temperature between the ground floor and the upstairs hallway.
• Two small bedrooms and one master bedroom on the upper floor each have one 4" x 10" vent register.
• The ground floor has two output registers on opposite sides of the floor.
• The basement has two registers, one in the laundry room and one in the basement proper (which is carpeted and insulated like the living room).
• All output registers in the basement are closed year-round.
• Output registers in upstairs bedrooms are usually fully open, but I close them in winter when temperatures are about 45 – 60 F outside, because the occupant of the ground floor keeps requesting the system to put out heat, which makes upstairs uncomfortably warm, especially on the side of the house that is directly exposed to the sun (my bedroom). I leave them open from spring to fall when temperatures are usually warm, and also leave them open when it's very cold outside (because the extreme cold of the outside temp overpowers the seeming "greenhouse effect" that ordinarily makes my bedroom unbearably hot).
• Playing with register open/closed status over the years hasn't seemed to make much of a difference. For example, I close the registers using the switch and put a strong magnetic sheet on top of the register when I absolutely don't want more heat coming into my bedroom, yet it continues to get hotter and hotter from about 9 AM – 7 PM on a mild winter day when temperatures are around 45 – 60 F.
• The heat of the sun probably plays a big role in why my room is so hot. The whole side of the house and the roof get belted with sun; solar energy companies are salivating to install solar panels on our roof because we're in the top 5% of solar power production based on our geography and building height relative to nearby buildings and trees.
• I didn't see any dampers in the HVAC / furnace room.

Unfortunately we don't really have a place to put a second HVAC system on the upper floor. We're already planning to take up more space by moving our laundry equipment from the basement to upstairs to eliminate a 2-floor haul every week (it's hard on my mom's back).

My solution might end up being to just install an A/C unit on the window sill upstairs and use a space heater as necessary. :/