Does it still stutter with the air filter removed?
BTW, Honda procedure is to replace the air filter on a yearly basis. With 34 years on a paper filter, you've gotten more than your money's worth.
The paper fibers collapse over time, making it progressively more restrictive. This "chokes" the engine. The running malady symptom I call "burbling".
Further, the bike is supposed to get a complete tune up every 3000 miles this includes cam chain tension and filter renewal, so you have answered several questions wrong. Have you found everything the Previous owner did to the bike perfect? Your confidence that the carb sync (part of a general tuneup) is high then?
After-market mufflers *can* also make carb tuning a challenge and different from stock Honda settings, but not always.
I'd focus on the air filter first...
Lastly, this tech forum is for SOHC4 bikes, not twins. So, this thread belongs in "other bikes". I'll ask the moderator to move it.
Cheers,