If it was up to me, the choice of replacing two gears that are obviously shot and cost less than $10 compared to replacing a $200+ part that is probably not broken is easy. Its pretty hard to screw up a govenor. You already have to pull the rear cover to replace the drive gear, but once thats done you're finished with the hardest part. Replace the small gear on the govenor itself, button it back up and test it out. If the govenor is bad, you'll know right away. Going back in to replace it is easy enough to justify the time spent.

Just my opinion, but you might want to give it some thought.