This has been a good exercise, and I will continue learning about the cryptography, but I'm really looking for something the average guy can use (i.e. me) to easily assemble Shamir's Secret Sharing keys into a Bitcoin WIF private key, does this not exist?
I couldn't resist the temptation, so here it is now:
https://mycelium.com/assets/entropy/checksalt/sss.html.
It's not very well tested yet, though. Also, as far as I know, iOS does not fully support in-browser video/image capture.
YES! This, exactly this.
Have not played around with it yet, will try later today, thank you very much for your efforts.
Drop this on a USB key stored with each share, and a copy in the cloud just in case, and Entropy's SSS scheme is now a long term viable solution for coin storage.