My 06 Fz1 started surging intermittently and back firing at times turned out to be my spark plug coil caps they were letting the spark leak out through them to ground.
might b something to look over and c if you can see a carbon spark trail.
I to had a bad coil some time ago on my 06 and it caused a random miss at high load. But for a rough idle I would get the throttle bodies synchronized as if they are out of sync it effects the lower rpm the most and the bike will still pull fine.