Thawing and refreezing is not intrinsically ruinous. If they aren't freezer burned (you'll know it when you see it) and don't smell funny when you thaw them out, I'd say they are probably fine. if anything, they ought to be more tender from ice crystals forming and maybe breaking up some tissues.

Yup, the remedy for this particular problem seems to be "get a new fridge". Working well for me so far! As a bonus, we can now walk past the fridge when the door is open, which we couldn't before. Makes actual food preparation so much easier!