Is it possible to route different applications to different audio outputs with Pulse Audio?

Yes, that's a built-in feature of PulseAudio. Various PA-compatible "volume mixers" such as pavucontrol or ponymix will let you assign a different output for each program (assuming PA actually recognizes those outputs as separate).

Try Ear Candy. It is not only possible to switch between outputs when they're attached, but also to route several programs to other outputs as you're looking for (and lots of other small improvements).