Based on the reasons behind not inviting people to a Bris (Why do we avoid inviting people to a b'rit milah specifically, and not other celebrations too?) why don't we just invite Moshiach Ben Dovid to a Bris, thereby forcing him to attend, and then requesting he reveal himself and end Golus already?
At the beginning of the procedure of Brit Milah, the Mohel invites Eliyahu HaNavi to come and help him.
However, the gemara says that Eliyahu is supposed to come before Mashiach.
Therefore, Mashiach cannot be invited before the Brit Milah starts, and it would be rude to only invite him in the middle.
It says in Yoreh Deah 265(12) that if there will be people at the seudah who are "אינם מהוגנים" - not so geshmack - one would not go eat at the seudah. Since I would certainly be at my own son's bris and seudah, I don't think it would be right to put Moshiach ben Dovid in that position.