At the metal air register is the coldest point from the unit mixing with hot/warm air causing condensation.  

Is that from back dripping condensate leaving the cooling coils?

Have your AC guy go out in the Spring and clean it out, check the refrigerant levels, blow out the condensate line, make sure everything is in tip top shape.

anyway you can create air flow in the basement,, one side in and one side out within a basement window.. this would sure help.. even a fan on the floor could help move the air. self draining dehumidifier is great except they run constantly and is big electric usage.. another thing is to wrap cold water pipes so condensation is kept under control so it doesn't drip.. 

Mini splits are ductless (air sourced)heat pumps.Depending on what you are trying to to accomplish they can be thousands of dollars but typically not.Keep in mind they can only provide heat usually efficiently to only a certain temperature since the condenser unit is outside and has to extract heat from the air, so if it's literally zero degrees outside it's going to be harder for it to extract heat.  

Client to choose color 936 1.50 1,404.00 Completion Package for: light bulbs interior exterior ,all new doors stops BN, cover plate, all new outlet and switch plate covers. 1 350.00 350.00 Replace all doors and hinges 7 doors 7 125.00 875.00 Smoke detector in each bedroom 2 35.00 70.00 Replace 7 door knobs 3 private 4 passage BN 7 45.00 315.00 Hvac New Hvac system 3 ton this system includes furnace, evaporator coil/air handler and exterior unit 1 4,687.00 4,687.00 Nest thermostat 1 500.00 500.00 Add cage to exterior condenser 1 500.00 500.00 Flooring Sand and finish all hardwood floors 750 3.50 2,625.00 Tile kitchen floors and bathroom floors 200 7.00 1,400.00 - Laundry room Plumb washer hookups properly and add new spigots and trim box before new drywall 1 375.00 375.00 - - - - - - - - - - - - - - - - - - - - - - - Estimated days to Complete 63 TOTAL $48,597.00

After the inspection, it is brought to my attention that the one of the furnaces, one of the water boilers, and a condenser unit for the AC are all really old and past their prime.

Plus you'll need to run a 220 outlet for the outside condenser.

Because the Thermostat is turned so low, a lot of condensation is forming on the ductwork inbetween the first floor ceiling and the second floor floor.  

Would you call in a handyman just to clean it up and maybe put a drip pan where the pipe is developing condensation?