Should I suspend a shelf from the ceiling?
You COULD do that, [the adjusters-things you want are called turnbuckles] but it might be a lot simpler (no holes in the ceiling) to use better and larger shelf brackets. Better, in having a brace that makes them a triangle. Larger, making a larger, more stable triangle. A pair of good heavy duty brackets in a large size will make a shelf that you can sit on and not deflect - much less a measly projector. I had a clothes dryer mounted on this sort of bracket for years.