I had my gas furnace & AC unit replaced in November, by my HVAC guy who's done 6 figures worth of business with me over the years and gives me preferential pricing, and it still cost me almost $6k for a higher-end unit and that was with no ductwork requirements.

If the hvac is a forced air system, perhaps it may help to clean the duct work.

Personally I have decided to suspend any repairs unless urgent.I have one tenant that needs new ductwork scheduled this Thursday.  

A large opossum managed to get into our ductwork, and died between the walls that were used as a plenum for the heating system! 

Can I mount this 4” pipe basically at the grate of the air return and run it through this air return (just drywall) until it hits the basement ductwork?  

The results seem promising but I have yet to sit down with them to talk numbers since there is a lot of variable cost based on the level of finish, lot condition, and then hiring a 3rd party to finish out the final details e.g. making final electrical connections, connecting plumbing to main drive line, running duct work etc. 

We lived in our St Louis duplex for 3.5yrs and in that time: tore out the plumbing from basement to roof and put in a 3rd fl master bath, retro fitted 3 separate HVAC systems with ductwork, and had all 44 windows replaced from basement through the 3rd fl - all while living in the unit and managing the renters downstairs...little bit of PTSD there!

Account Closed well if you have the space to run the duckwork or eventually put a forced air in unit to avoid unnecessary runs of duct work from basement then fine.

Additional ductwork will need to be ran to a few rooms. 

When they vacate you'll need to wash all the walls and ceilings, possibly re-paint, and clean all the ductwork because of their habit.