I have actually seen a fixed-wing aircraft fly backwards.
As an ant,on camp at RIC, watching a Bou do a STOL approach the short little grass cross-strip they had back then, into a reasonable headwind. Full flaps, the lot, barely making ground. Then a stronger gust came in and the thing actually retreated about a body-length. Then cam fun & games with the p1ssaphone and stories of hanging over the back with arses out, fertilising the land below... though I suspect my legs were being pulled on that one.
As for rear-end birdstrikes, the Catalina would be a candidate for that as well.