Mounting a projector underneath a soffit containing ductwork

I’m looking to install a projector in my basement and the most ideal configuration would be to mount it to the ceiling with a ceiling mount. However, the “sweet spot” location for hanging (in considering distance to the projector screen) falls underneath a bulkhead that houses AC and heating ductwork, and I don’t detect any beams with my stud finder.

I obviously don’t want to mount directly into the ductwork for many reasons (vibration, projector misalignment due to changing temperatures expanding/contracting, air leaks, etc.).

What are some other options? The projector is only 8 lbs., so can I use construction adhesive (like liquid nails) to adhere a piece of wood onto the drywall, and then mount the projector into the wood? The projector mount includes 2.5” lag bolts for mounting…

I’ve also considered a projector shelf on the back wall but given the distance to the screen, the projector lens should be 28.24” from the back wall – so that would be a very deep (and perhaps custom built) shelf.

Here’s a picture of the area. Thanks!