Idea: Make a new mode in group finder. "Marathon mode." Or name it whatever. The idea is that it ques you for random dungeons with everybody else looking for groups, but each time you complete a dungeon, that particular dungeon is checked off the list for the rest of the 24 hour cycle (only for the purposes of this mode). So you keep doing randoms, but you never do the same dungeon twice. The random dungeon rewards build as your count of completed dungeons grows higher. You would need to program it so that it remembers where you left off for that 24 hour cycle so people can take a break.
Reasons: I love doing random dungeons. I hate getting the same one over and over on pledge day. It would be really cool to build up to some neat rewards and see how many dungeons you could do on a day off. It would get more people queuing for randoms rather than particular dungeons they need. There are zero reasons not to do this.
Sound fun?