CH Ignition on BME 44 Problem
I had the exact same symptoms last year. Engine started and ran great for exactly three minutes and then it ran crappy and acted like it was alternately going way lean then way rich. I tried everything, put a kit in the carb, swapped tanks, ignition batteries, ignition switch, you name it. Sent the engine in twice, both times it came back with a message that it ran great on the bench. Didn't run great on my bench! Finally talked the ignition mfgr. into sending me a new module which I installed. Problem solved immediately.
After you have exhausted all possibilities, try another ignition. CH are good people and they might send you another module.