You can see a brief biographical summary of the judges here.

So it would seem one Reagan appointee, One Bush Sr. appointee, and one Bush Jr. appointee. Two of the judges seem to have spent a lot of their legal careers in areas less favorable to gun control. Overall I'd say we could have a fair chance of prevailing here. Anyone know what "General Advisory Committee on Arms Control and Disarmament" is about? A little initial googling seems to indicate it was more a cold war disarmament committee rather than "let's take all their guns" type.