the current paper backups already store 512 bits. Thus, if you split your paper backup into 3-of-5 like my example above, in order to recover the secret you'll be typing 3 kB into Armory by hand!
3 kB as in 3 kilobytes? I don't know what you use to encode the bits in a paper wallet but if you use base 64 you'll get 6 bits per byte, so should only have to type 171 characters from each of the backups, or 513 characters in total.
Wtf. You're right. I can't believe I confused myself with bits and bytes!
But my point of reference was still correct: I know that typing a regular paper backup is "annoying", so typing 6 times as much would be more than "annoying." Granted, I use hex right now, and should probably use base 64 instead as you suggested. Though, part of the reason the paper backup uses a different alphabet than normal hex is so that it's easier to touch-type, since most people don't touch-type numbers very well. If anything, I'd probably switch to base-32, but then I'm not gaining much over hex...
On a related note, can someone please find for me one of the few largest 512-bit prime numbers? My lookup table of primes stopped at 400 bits, and I haven't been able to find an appropriate one for 512. Having that would make it much more straightforward to fragment the current paper backups, rather than fragging the root key and chaincodes separately.