The upside-down Jesus is so the birds can perch on it, look down and read it right-side up. I fear the problem is that it advertises a "come to Jesus" meeting and your are just going to get more birds as The Word spreads. Now an upside-down crucifix might put the scare in them, but you'd probably start losing neighbors at that point, too.
Let me suggest that the birds, or any animal, will habituate to anything that's there long enough and doesn't make good on a threat. You might have to switch things up every once in a while to keep them off their game.