Still no luck with the dragon, so I thought I'd try my hand at the annihilation again. And this time I took all the advice I got earlier and combined it. Sort of.
Looking back on it, that was way too much overkill, but I wanted to make sure I didn't have to get through 400 enemies again. The ratman died in 3 seconds after being teleported by Yu into Shamare's doll and getting beat on by the bun and roach.