Now that you mention this, is there any advantage at all over the 24 word backup to the 12? I've heard that there's really not much difference in terms of security, but I see lots of comments from folks who subscribe to the "more words means more secure" mindset.
The more the words, the longer it would take to brute force. That is the advantage. But both 12 and 24 words have 128 bits of security because bitcoin private key has 128 bits of security. The security which is enough for your coins protection.