Does it make a difference how the pressure differential is set up? In an airplane wing it’s set up by the length difference of air traveled due to the shape of the wing. The airflow direction only matters here because it’s necessary to provide the forces used to create that difference on a shaped wing.
What if it were possible to create a pressure difference in some other way on both sides of the wing? Would there still be lift? Your example of blowing a fan under the wing might actually be somewhat valid. (Just not valid enough to fly a plane.)
On our sailboat the difference on both sides of the sail might be set up by air being slightly more compressed on one side by a powerful fan.

Occam’s precession force idea might be proved by rotating a giant flywheel instead of a fan on the back of the boat (light enough not to sink it, of course.) I would think the boat would need a keel for this to work.