The existing ductwork couldn’t accommodate this size hood, requiring new ductwork ran to the roof.  

You can easily burn up more labor reworking the ductwork than system install, which is really plug & play.

The single-family property doesn’t have any existing ductwork, so we’re planning to install a multi-zone mini split system (4 zones).We’ve received three quotes so far, ranging from $18K to $26K from HVAC companies.

This may involve adding ductwork, installing a separate HVAC unit, or using portable heating and cooling units.5.

In the City of Philadelphia, you will also have to have an extra electric meter to serve common areas, such as lighting and fire alarms. http://www.biggerpockets.com/forums/84/topics/7504...Since you are doing a gut, now would be the time to get the ductwork for both supplies and returns into place.

Brush up on building code requirements: in basements you're looking for egress windows that are 5.7 sq feet or more openable (3ft by 3ft casement style windows work best), and ceiling heights 6ft 8 inches or greater (as little as 6 ft 4 inches is ok under ductwork and beams though)3.

@Heath D Wallace The first thing that strikes me as odd is your explanation on the work being nearly complete, yet no duct work followed up by your second post that the original contractor is completing finish work while the HVAC contractor you selected is completing the HVAC scope.

How about the HVAC and ductwork system?

I've got a few properties that would really benefit from updated heating/cooling systems. 1 duplex I have has electric baseboard heat / window AC (Old 1880s property, no crawlspace or basement, no existing ductwork), another I'd like to add central air too, and a 3rd that has old gas wall furnaces / window AC that I would replace with mini splits (again no ductwork). 

We installed a new truss system to allow proper attic space for ductwork, added a metal roof, replaced drywall What was the outcome?