Of all things mentioned ... the pick-up coil goes to the top of my list. If you read the 11 million post BIG DR650 thread ... you'll see that over time there have been several failed pick-up coils (also called "ignitor or Pulse coil). Not many, but a few. One was on Big Al's bike which failed somewhere in Cent. America. The local mechanics borrowed a PU coil from a car and fit it in .... IT WORKED!
You're correct .. The PU Coil is part of the Stator. It's rare but there have been a few over the years.
I don't believe the carb is the issue. (unless it's been buggered up by someone trying to "fix" it!
We've never seen a Main coil go bad on a DR650. There have been a few Stators gone bad but most times it's misdiagnosed and turns out to only be the Pick-up coil.
One or two bad CDI boxes too ... but once again ... very rare. On the road I carry a spare Stator.
Best of luck !