So because the design team didn't release things that would make Biggs OP he's not a problem?
The fact that the design team has referenced him multiple times as a problem is THE problem with Biggs. We don't know what design space he's blocked off; they do know and don't like it.
I think stress shut down could work. You could also make his ability take an action or require him to spend a token, automatically takes 1 damage ala Xizor... lots of options and I'm for whichever one opens up the most design space for him.
Or to completely rewrite his text (in a theoretical x wing 2.0 situation) have him be able to soak one damage away from attacks targeting friendly ships, friendly ships within one count as obstructed, takes damage if those obstructed attacks miss etc