True enough -- on a 335, the "wings" have very little structural intent. This is fine for players who mostly sit or stand still. Actually, unless you're already endangering your guitar, it'd likely do fine with a well-installed wood screw, but I do understand your concern.
Two options come to mind. The easiest is to overdrill the hole (like 1/4" or more), & put in some sort of toggle anchor. Not a big fan of this one, I'll admit.
That leaves (as you guessed) going inside. If I needed to do THAT much work, I'd drill the screw-size hole clean through & use fishline, pulling the screw through from inside. The little piece of wood would be carved to roughly fit -- short of taking the top off, or much painstaking work with a bore cam, I doubt exactness is possible -- & get a thin layer of black rubber foam where it'd mee the inside of the horn. Instead of a screw I'd use a hexhead, carve a snug hex recess into the wood, & use a tiny dot of cyanocrylate on the screw to to pull it into place; this would likely take a few tries to get the screw length correct. Put on the strap button & a nut (maybe with Loctite).
