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Choice 3: Exemplar to an appropriate level Hero and help them get XP (and work off your debt) while you both get the badge. I know... it's just crazy enough to work.
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I think you have an excellent point, however, the risk vs. reward for Exemplar is way out of whack. As a lvl 23 scrapper, I exemplared to a level 19 defender to do a clockwork mission with him and a couple of level 17 friends. In one location, the mission had spawned seven (7!) level 20 bosses, mostly Assembler and Cannon Princes. In one hallway, all standing right next to each other. After a couple of deaths, I finally un-exemplared, cleared the area, and then re-exemplared to try to work off my accumulated debt. By the end of the mission, I still had a few thousand in debt left.
The influence rewards for Exemplar are pretty pitiful, too. At level 23, my SOs are 30,000 infl. each. I received approx. 20-30 influence per defeated mob as an exemplar. This is a pittance, I mean, really. As an Exemplar it's just as dangerous as a natural to throw yourself into a group of yellow mobs, but I'm rewarded by getting 0.5% closer to a single SO.