> All right, 13 -> 14 is driving me crazy, and since everybody says it's lame I have low motivation to keep noodling at it. Any hints? Just nudge me toward the right ballpark, please.

The clue is the beginning of a three word expression, which can be found on the Wikipedia page for the number (not year) 13. Use the two remaining words, separated by an underscore.

The reason it's so stupid is, besides that it's a super obscure expression, is that it doesn't involve expressing the number 14 in the manner that 13 is expressed, which is how every other puzzle in the sequence works. It's really strange.