First, realize that with a single zone system and multiple floors, it's difficult to get the temperature correct everywhere. Also, since you mentioned this was an attic space, you're likely against the roof and getting heat from every wall plus from the computers and people in the space. In short, you're fighting a losing battle.
I've got a similar challenge, though not to your extreme, and here's what I have done. First, learn how to adjust the baffles on the ducts. In the summer, you want as much as possible going to the high floors, and the reverse in the winter. Get someone to feel the air coming out while you're pushing the baffle all the way to one side or another. For me, it made little difference until I pushed it all the way.
Next, exclude any rooms you don't need to heat/cool, e.g. a guest room or storage space in the basement. Shut the door and close the vents to reduce the effort you're putting on the HVAC.
Finally, I swapped out my return grille with models that accept a filter (they are hinged and open after releasing two small clips). These return grilles are special orders from the big box stores, but they carry them. I still leave a thin blue "rock catcher" filter directly on my HVAC blower itself. And I put a filter in every return except the upstairs in the summer and downstairs in the winter. The idea being to suck out as much air as possible from location that needs it.
This means that switching between heat and cool is a process, flipping the baffles and swapping in and out filters. But a little effort is better than a lot of sweating.
One last suggestion, since it sounds like you're running a small server farm in your attic. Either move that down to the basement, or consider replacing the window unit with a ductless mini-split system. You get to see out the window, and these systems have configurable thermostats.
You may look into installing a vent in the furnace room if you have one next to that area. This may allow you to draw heat from the furnace room, into your finished basement area, up the stairs to the first floor and back down again. Depends on where the return is and how things are "zoned".
If you do install on the drywall get as low as possible so the heat sweeps across your comfort area to the nearest return. Heat rises... Install dampers so you can tweak the amount cool feeding into the basement during the summer. Follow the path of airflow and calculate as much as you can. In tools such as Revit (warning: steep learning curve) it is called a load analysis; though, it can be done back of the hand.
If you already have a ducted system, I wouldn't install an electric heater. Nice for a small area such as a desk/bathroom, but do keep in mind how they affect humidity.
Best Answer
Flex pipe is the lazy way to put in ducting. I think it should not be allowed for trunk lines and yes you were told correctly it is not as efficient because of the turbulence. I am guessing this was a diy home because of the cobbled sections of round pipe to flex duct in the photo. Unfortunately some use it more than others I only use it for short sections from the trunk to the registers. Installing regular pipe will improve the flow the longer the flex replaced the bigger the improvement in flow you will see.