Just have a draw every single week. The list comes out at 3 PM, you have until midnight to apply (or the next day) and then just run the draw immediately, those with the most points win and you use your points. Seems pretty simple to me. Only charge a card if they are successful and make it minimal to enter the draw, $5. If no one wants the tag sent it to the leftovers pile. If your credit card doesn't work, go to the next in-line.
If you have 2 months to plan the hunt, more people will use more points, if you have 1 day to plan a hunt or like last week (hunts had already started!), then less points will be needed.
This would be a lot less exciting than this year's system, but much more fair and you burn some points up at the same time.