I've been thinking about this for perhaps too long. What if you could change an ID's faction during deck building? Do any ID/faction combos break the game? Is this interesting enough to try at a club night?
Criminal Kit or Quetzal would probably be strong.
Anarch Andy might be very good.
Noise almost certainly doesn't move (though actually you can probably import enough viruses if you can use all Shaper's Glue)
I haven't thought as much about corp side. I think the good corp IDs are spread about pretty well. NEH might be a fit for shell game Jinteki, but probably isn't as good as PE at it.