How do I clean heat ducts buried in a concrete slab floor?

You really need a pro with top notch equipment for long “runs”.

Afterwards, you maintain yearly.

I would try spraying Lysol disinfectant deodorizer into each of the cold air return vents while the furnace/air conditioner is running. It should pull the Lysol through to kill any mold or mildew. Worth a try and it's a cheap fix. I read a long time ago that you can do this to your car also. I park under a carport and in the summer with all the heat and humidity, I get the same thing. In this case, you turn on your defrost and spray the Lysol directly into the vent on the outside of your car near the windshield. It works great!

Vaccum

Shark! Love mine

https://www.todayshomeowner.com/hvac-duct-cleaning-scam-or-worth-it/

At the bottom of this article is the name of an organization of air duct cleaners. Maybe they can recommend someone when you give them the scope of your problem.