If you want some help, I know a very good mechanic who lives about 30 minutes from Conyers, GA who has flathead experience. COVID has him only working 4 days per week, so he may be able to help. Let me know.
The reason I ask is because I recently had the similar symptoms on my '36 coupe. I had let it sit just a little too long, or so I thought. I hadn't cranked it in a couple of 4 months. When I finally got it to crank it was running really rough and backfiring. I thought it HAD to be gunked up carbs even though I always use the real gas. No corn gas for my coupe.
After a fair amount of scratchin' my *** I finally broke out the timing light and discovered that 2 of my plugs were mis-firing really bad. Now keep in mind it was running perfectly the last time I drove it. Plugs looked good but were just intermittent. Why??? I don't have any idea. But a new set of plugs solved my issue.
Even if a plug would be dead or the carb is full of gunk they usually just miss...
Bucking and backfiring is usually condensor or arcover in rotor/cap.
After changing condensor i would carefully inspect all distributor parts before starting to tear down and change more parts.