Ditto on all that!
SHB are in my hives, they're a lot like strep or staph...always around but usually only an issue if the health is compromised. They haven't been an issue in any of my outdoor hives.
Yup, wood and plastic, got 'em both! On the bright side, the topbars of the plastic frame won't pull off!! I've had the wood frame do what your's are doing. I wrapped some wire around top to bottom (I have frame wire, but other would probably work too), worked like a charm, I think that frame is still working.
I don't use feeders much any more. Hive top feeders are awesome in the fall. But if you want to feed now, maybe retire the hive top feeder for now and use jars with holes on top of the frames, a package don't need a lot of feed.
Don't have any advice on birds....