Haha, welcome to my world. It is real bizarre. I can't get anything out of it, either.
The video I have is on Pkmn Stadium during a stage change, which does hurt the credibility, although I/he was thrown before the stage changed and we weren't any any part that moved (it was the part with the trees and we were on the bottom). But yes, the one video I have at the moment is during scenery change. It has happened while I was Ganon vs. Mario on Smashville on the normal stage (not the platform), and it does not get much more generic than that. I don't recall the other stages, but I only play on the very neutral stages typically. If my brother sends me the other video and I find some means of uploading these (.bin files are no good), then I'll put them both up.
Actually, Kyle if you add me and give me your Wii code, I could just send the replays to you and tell you when to look out for it. Does that work?
I am basically out of ideas, too. I haven't tried many of the things you mentioned, and those were some really good ideas. I had never thought of those. I did consider special button combinations like you mention, but the thing that is really strange is that when I did it vs Ike in the replay I have recorded, there was no time between grab and throw basically. He grabbed and instantly bthrew me and it was reversed. I mash buttons pretty fast, but not fast enough to input a precise button combo in that short span of time. I was thinking maybe it was something like tumble cancel where you just mash left and right without any up or down component, but I was spinning the sticks. Even testing just horizontal or vertical components yielded nothing productive.
I don't know what else I can try by means of explicitly testing this, but I'll continue to keep my eyes peeled for some other occurrences.