HVAC work is so expensive relative to the cost of the furnace, ductwork and material, I would go new as well.  

Wiring, plumbing, all exterior and windows keeping minimum interior trim and duct work. 

Due to a heat duct that runs floor to ceiling in the wall, I plan on extending the doorway opening from three feet to six feet and leaving the duct work in place to save time and money.

@Seth Mosley In my experience, John T Reed's article is very close to reality. 45-55% is a good rough estimate of expenses + capital expenditures.As you talk to experienced investors - those that have concluded the irrationally exuberant period that seems to affect every SFR investor at the beginning (me included) - you will find that their true cash on cash returns are a lot lower than anyone cares to admit.A few months ago I replaced an HVAC system ($4500) in one rental and ductwork ($3500) in another.

The reason you may hear the sound on an interior wall rather than exterior, when temperature change is a factor would have to do with where the tension release point in the joined materials occurs.That said, given your temperature changes are not extreme at the moment, If you have forced air heat, I would first explore the possibility the sound is HVAC duct work in the wall/ceiling (as Billy Bob suggested).    

Used good 1/2 inch 8lb pad.Kitchen: Cabinets, appliances, sink, countertop and bead board paneling 2,300Plumbing, new water heater 2800Electrical upgrades: 1800New deck: 1600Bathroom: sink, commode, shower surround, bead board paneling. 400All new lights 450Dumpster fees (3 30yd) 1200Clear the yard 2000Other landscaping 500New furnace and now duct work 4000Paint exterior 350Paint interior 350HAHAHAHA oh man I'm depressedSo the numbers will look like hell but in 2 yrs it won't mean much. 

It's going to depend on the number of drops, how easy it is to run duct work (a large attic will be favorable), electrical (do your existing panels have the capacity to add central? 

There is no traditional "duct" work going thru the wall.

Duct work also stolen from home.

The A/C UOP is made up of ductwork and the A/C unit and it's parts.