I've used RMB heating and cooling to do all new forced air unit as well as all new duct work.

Have you found any quality Duct work cleaners in the meantime?

I also have a brick front , and it sucks up the heat  ( great in winter)  My front door in the late afternoon , if you touch it you will burn your hand .It was worse until I added a vent fan in the attic and I tinted the front windows , I also have a window unit in 1 bedroom so I could balance the ductwork to send more to the living areas. 

Depending on the house construction, insulation, etc. this can be an expensive process to install all new ductwork (do you have access) and equipment.

No duct work at all makes for an easier conversion.

To give some context, what I'm needing done is as follows: roof repair, 3-5 floor joists replaced or "sistered", surface mold remediation, 3 bathrooms remodeled, hardwoods sanded/buffed/finished, exterior and interior paint, drywall repair, granite countertops and new appliances in kitchen, new HVAC and ductwork, branches cut away from roof, gable vent repair, insulation.  

I am planning on putting in duct work for a natural gas unit to heat the main floor and the new basement remodel (which will all be one apartment).My question is what should I do with the upstairs apartment?

And, if the home doesnt have ductwork in the crawlspace (unfortunately mine does) theres less of a need to have a lower building deductible in my opinion... also think it's smart idea to get HVAC raised up. 

If it has amazing cash flow, a new heat pump system installed even with ductwork is going to cost you under 10k in NC (I'm in TN) and factored out over time is virtually nothing.

I made use of about $10k in taxpayer-funded rebates for mine, so the final bill was "just" $26k, and taxpayers also partly picked up the bill for the ductwork because of how the local laws were written, which made it the same price as a regular system plus ductwork.Check out the new direct exchange geothermal systems.