Without enclosing the front of the projector in a boxing setup, you're not going to be getting much noise deadening. Foam underneath the projector can help if you're getting vibration noise issues, but covering five sides while the sixth is the one that faces the room won't really help, especially with the size of that area. The foam would absorb the reflections going sideways and backwards, but the issue is that you still have noise coming straight forward.
If you feel like taking a shot at putting something in there for the rearward and side reflections to see if you like it, you wouldn't be doing much better one way or another with only a ½ difference between the eggcrate and sheet foam you already have, so you definitely don't need to buy the eggcrate. If you somehow have reflections from your speakers getting trapped back there and causing issues, that's another story. But for handling the noise of a projector, you'll probably want a hush box as Big said.