Santa Kona seems to have the ideal solution to this problem.
I am actually surprised that the maker of the Marine badge did not foresee that it would arise.
My regimental bonnet badge has two solid screwposts on it. On occasion they have seemed too long, but rather too long than too short.
As for backing, I found some abandoned, cut-up leather belts lying around the barrack room the day I finished my initial training. Taking a piece of a belt and placing it behind the badge provided me with a solid support for the badge. It has always stood upright as it is supposted to do.
Regards,
Mike