I'll hope that responding to the random idea part won't completely derail the topic.
Naturally I like the idea - Sacosphilz knows I like puzzles - but I'd suggest a slightly different spin to it. You mention a small additional reward, which I assume you would receive only if you solved the puzzle. What about a large reward if you manage to solve it quickly? It could prove to be an interesting way to Balance the differences in wait time. Choosing the time interval could serve not just to demonstrate patience, but act as a bid towards how quickly you think you can solve the puzzle. Bid 1 hour and solve it, and get a bonus perhaps comparable to having waited 24 hours. Fail to solve it in that time and receive only the standard bonuses for 1 hour. It could be like "briskness for story mode".
If you bid 24 hours and solve it in 1 hour... there are at least a few options to choose from, and test what seems most balanced. I would think that basing the puzzle reward strictly on the bid might be best; getting two large bonuses might really throw things off. If two people bid 24 hours, one solves it in one hour and the other solves it in 23 hours, is it fair that they receive the same bonus? Maybe you get to advance the story after you complete the puzzle, or only have to wait half of the time remaining.
Feel free to move this post into the suggestions topic, but I wanted to give credit to Sacosphilz for "planting the seed" as it were.