I think that this was fun, if nothing more than to remind me of my engineering physics classes in the early 90's, when we investigated this motion.
I am quite sure that the extra energy "absorbed" by the lure by towing it in the water will overwhelm the very minimal unstable motion due to the Dzhanibekov Effect. Still, the TRUE scientific method allows us, even requires us, to consider alternative interpretations to what we think we know.
Thanks for the mental exercise, but I don't think I will be joining in on the development and design on this one. LOL