So I read something on Reddit. Not sure if it works or not, but I figure it can't hurt to try, right? The theory is that for Epic and Legendary tokens every time you don't get one, you get a boost at success at the next one. So all these failed drops are building up for a good chance... and then instead of getting it for the Event Character token, you get it on one of the other characters you are working on. So instead of a Miss Piggy Ear Hat dropping you get a Horned King Ear Hat. So the suggested strategy is to only send characters who can collect tokens out for Miss Piggy and people working on common / uncommon tokens (not sure how Rare tokens fit into this boost, so I figured not to chance it) not the more difficult tokens.
In my IOS game, I went from 4 hats to 9 in the last 24 hours. Still waiting for my Windows drops in the next half hour. Maybe that is just RNG being in my favor, but again... it can't hurt to try for 2 days.