This is a question for a local HVAC company, and a contractor. A waste of time with any other method. : )

A "standard "duct is 12 inches and rigid. You need other options, and need local help...............and smaller duct, no matter what.

https://www.bobvila.com/articles/mini-duct-hvac/

Look into -

https://www.unicosystem.com/

Or

https://www.spacepak.com/

Unico is the advice and mention in the Bob Villa link, as well.

A depth of 12 inches would allow sufficient height for duct work. I assume the ceiling joists are 16 inches on center. The problem is opening up the ceiling to run the duct work and running smaller ducts perpendicular to the joists,

Thanks, all! I’ll call around and mention those systems. Really appreciate the guidance here.

In SoCal, it's not unusual for an HVAC retrofit to a flat roofed house, to modernize heating and often to add cooling, to put equipment AND ducts on the roof. It's often done at the same time as a re-roofing to be sure the roof penetrations are well sealed.

If the house is on a raised perimeter foundation, I don't know why you wouldn't consider putting the equipment in the crawl space and the ducts there too. The supply ducts then are cut into floors - this is a very common approach too.