With the stator out, I put in my order for a new Ingitech unit and a rebuilt stator from Custom Rewind. I also ordered a full seal replacement kit.
I returned to the bike and began cleaning out the carbs to restore them. To my surprise, under the grime on the outside, the carb interiors were remarkably clean! My intent was to remove the air box and install cone filters, so I also got the old jets out and put in new ones. I put in new 90 and 120 jets, and replaced seals throughout the carb.
While cleaning the carbs, I decided to use some compressed air to blow out areas I couldn't get to. I hadn't removed a small rubber plug that gets squished down when the carb top is on, and with the first jet of compressed air, this little stopper ejected at light speed and shot across the shop, never to be found again. After hunting the internet to find a replacement for this little guy, I discovered that many people have made this mistake before me and have used Bic pen butts to temporarily replace the lost part. Since I had ample time while the stator shipped, I went ahead and ordered a few new ones that one of the forum users recommended.
The rebound spring for the butterfly valve on my carbs was wired in place instead of fitting around the post where it is intended to sit. To fix this hack repair, I took some string and threaded it past the post and around the hooked end of the spring. Pulling and wiggling, with great effort I managed to pop it back in place, which gave the valve significantly more torque when returning to the throttle off position.