"Fail to find" breaks this card. To make it work properly, it needs a new wording.

"Target opponent may pay any amount of life. Search your library for up to X plus one cards with different names, where X is the amount of life paid this way, reveal them, and shuffle your library. That opponent chooses X of those cards and you put them on the bottom of your library in any order. Put the rest into your hand."

How does making it "up to" fixes the problem at all? Now it's the card itself, not the rules that allow you to find nothing at all! I was trying to avoid the opponent looking at the entire deck, but I'm starting to wonder if that's possible.

The rules automatically imply the "up to" whether you put it on the card or not, because of the "fail to find" rule. Gifts Ungiven was recently given errata to have an "up to" so that its Oracle wording alone will be sufficient to figure out what you can do with the card, even if you've never heard of that rule.

So my only option to make the payment be meaningful is to allow the opponent to look in the deck? The idea is that if an opponent pays, it ought to make the card less useful, but as is, they could pay all their life and the caster is still not forced to offer any extra choices.

The other option is the Signal the Clans approach. Make everything after the search conditional on finding enough cards.

With my suggested wording, you wouldn't have to find X+1 cards, but if you (voluntarily or otherwise) find anything less than that, you'll have to put back X (which is all of them), and the spell becomes pretty much useless.

@Sadistic OH! yes, that would result in pretty much what I wanted ^_^;;;