When my vacuum petcock died, it was putting gas into the vacuum line causing rough idle and stalling when I stopped.

I plugged the vacuum line. (both sides from the carb and the petcock)
put it on prime, the fuel flow was a small trickle compared to a normal full-on petcock.  Prime is really intended to fill the carb bowls...speed of flow is not a necessity.

The bike was easily rideable as long as the throttle wasn't opened too much.

The part about rocking the bike side to side causing it to die makes me either think fuel level in bowl too high or a wiring issue.

If there's crud of some sort in the pilot circuit, it will generally come on suddenly after it picks up the crud.  

I did notice mine idled a bit rough after the rectifier died and the battery voltage got really low.

Hope you get it figured pretty soon.

I purchased and installed a raptor 660 petcock today. Easy replacement, however the brass fitting to the fuel line is smaller than the one on the Suzuki petcock. Do I need to get a different Raptor petcock? How do I know if I'm getting the right one? Thanks.