So one interesting thing that I noticed when syncing the carbs was that cylinder 2 gauge indicated that vacuum was lagging behind the others. It would take longer for carb to drop and then return to the idle vacuum after I blip the throttle.
This hints of a leaking exhaust valve. It can be caused by either a pitted face, or a worn guide that lets it tilt when opened, causing it to momentarily close "later" than it should. When the engine is revved up, the compression in the affected cylinder drops a little as compared to the others, which then lets the others drag it along and lean out its fuel mixture, making it pop.
For a sort of simplistic diagnosis, try either opening the air screw on that cylinder only about 1/8 turn more than the others. If you're so inclined, also raise the needle in the slide by a notch for the same mixture change above 4000 RPM.
Sometimes, this symptom can come from a long-term misadjustment of the carb, like a too-high vacuum on the affected cylinder. If you have the patience, over a thousand miles or so these bikes can actually "heal up" a bit if the seats have lost their seal, because the valves do not rotate in these engines. This lets them pack some carbon into the leaky niches of the seats, making them seal again until, typically, a long hiway trip: that will blow out the carbon and repeat the cycle. If you were to take a REAL long hiway trip, holding it steadily at the 5000+ RPM of our 80 MPH interstate today, it will also tend to flatten the higher points of the seats and make them seal again, but I am referring to 500-700 miles per day for maybe a week at a stretch to accomplish this feat. I have done it, more than several times, with these engines, and it works reliably. But, it's a slow process compared to removing the engine and fixing it in a day or two.
The above "fix", however, does require that the valve guides are in good shape, not too loose, and not oval from wear (which happens on "F" & K7/8 engines and engines with high-lift cams). If the guides are in poor shape, it won't "heal itself". The K0-K4 bikes are the best self-healers.
I am a little concerned about a previous post: you mentioned that you have 657A carbs (unusual for the K3) and that they DON'T have tiny holes in the tips of the air screws. Something seems amiss, there: the primary difference between the 657A and 657B carbs was: the "B" lost the air screw holes and their mainjet went down to #105, and the needle clip went down to the 4th (from top) notch in the later K3 and the K4. The size of the hole in the idle venturi also changed, but it's real hard to gage that one.
