Solution for fiberglass ducts that have collapsed in basement

You want a second return in the ceiling of the top floor for cooling. Otherwise, all the hot air will collect upstairs and you'll have a very difficult time cooling the space. Any air return I've ever seen, that goes between floors, involved a wall being built out. Usually it's hard to tell because it's the back side of a bathtub that looks like it's built out for the bathtub to fit, or a closet that's a bit narrower. You may get lucky and already have space for it behind one of your walls, but that would require looking over a detailed floor plan to see.

Based upon the description, the hazard of asbestos has been present on the property for many years and most likely through multiple owners. To date the current owner has not moved to mitigate the hazard, either through ignorance of its presence or due to disregard for the potential harm that may result.

As renters, the meaningful options are really:

1. Convince your landlord to deal with a hazard.
2. Stay and live with things the way they are.
3. Move.

Perhaps your landlord remains unaware of the asbestos containing materials, in which case they should be promptly informed so that they may take appropriate action toward abatement/encapsulation. The Bay Area Air Quality Management District is the agency responsible for regulating construction related activities in your area when asbestos is involved.

Given the level of resources often entailed in proper removal of friable asbestos containing materials, proper removal is likely to be the source of substantial disruption to activities in your home.

A typical residential rental agreement may not allow a renter to contract for the scope of work required for abatement of the HVAC duct system. It would be wise to have your attorney review your lease before hiring a company to disassemble or partially demolition any building systems.

In the end, the home may not provide the sense of safety that people commonly expect without meaningful action on the part of your landlord and should it be necessary to consider forcing the landlord's hand as an option, the end result may not be worth the energy required.