Can I move warm air from 2nd floor to basement to help with heating?
I live about 30 miles north of Pittsburgh, Pa. so I am familiar with some of your problems. First: the office and basement should not be on the same zone. Since it is installed this way it may be impossible to change now. In summer the office needs lots of cooling to offset the southwest facing windows and the basement needs none or even some heating. Add returns, 2 or more, or as many as you can at the floor level in the basement, connected to the 1st. and 2nd floor unit. Do not disconnect the high wall return near the attic access, but add more if you can to take the hot air off the ceiling. Run the fan for this unit continuously, 24 hours a day on a low speed when the unit is not calling for A/C, to help recirculate the cold basement air.  Close any basement supply registers in the summer when the A/C is running. Consult a roofing specialist to see if it would be advantageous to add a roof mounted, thermostatically controlled, attic fan, to vent the excess heat from the attic area. You said that every room has cold air returns. Are there both high and low returns in each room? If so, the highs are used in the summer and the lows in the winter except in the basement. Multiple story homes with open stair wells, open to all floors are very hard to heat and cool. All the heat rises and the cold air falls, as you well know. In my experience adding Tjernlund fans to circulate air is just another noise you will have to contend with. Hopes this info helps. Good luck, in solving your problems.