You could just move it over, and try to cover the holes with what you are hanging. If you want it there, you could drill out and glue in corresponding dowels. Allow to dry, chisel and sand flush with surface. Drill pilot hole and screw. If what you're hanging isn't too heavy, typical wall plugs will work fine as well.

Give it a try on the wall first, you'll see what I mean. Good luck.

One thing I see often with DIY'ers is not knowing that most stud finders need to be calibrated when placed on the surface you want to find framing. Press it against the wall, hold it still, push the button and when you here "beep" then you can move it across. Sometimes you need to calibrate it in a different spot as you can't calibrate it over a stud.

I was just teaching a guy this at work the other day, he was watching me install some cabinets in a classroom and was admiring my Franklin stud finder, saying how his doesn't work. I pulled out my cheap 20 dollar one, and showed him how they need to he calibrated. Most stud finders work fine if you aren't going over plaster, double drywall, or a similar situation.

You could also use toggles of the projector isn't overly heavy. Or toggle a finished board onto the ceiling, round over the edges and paint or stain, then attach projector to that. A few toggles spaced apart over the board should leave nothing to worry about.

If you want it to be really strong, I would use 4x4 posts and "let in" (notch out) each post in the long direction of the table top to use with 2x6 for your top frame. So the 2x6 will sit in a notch in the post and be flush all around the outside. Shorter length on each end you could use structural brackets or beefy screws to attach, but in reality it isn't going anywhere. Once in place, you could carriage bolt them, or use timberlock structural screws or even some number 12 or number 14's. This way the load isn't being carried by the fasteners.

Hope this makes sense.