Prior to my 2013 rebuild of my K2, the #2 cylinder always waited 10-15 seconds to start running (cold) until the other 3 had told it to get with the program. It would run with the choke fully on, but quit as soon as it was cracked open. After it warmed up a minute or so, it was fine.
Then at the rebuild, I installed a [much] later cam, from a K4 with less than 6000 miles on it (mine had lost almost -0.4mm of lift on 2 lobes, intakes both, at 131k miles). The cold start was slightly improved regarding #2, taking only half as long to wake up. But, this has a tradeoff of sorts: it will not pull away smoothly until the engine has run for a full minute, and #2 is always the culprit.
Inside my carbs, the #2 always fills up last. I can remove the float bowls and turn on the fuel, and the 1, 3, 4 carbs immediately dribble while #2 waits about 5-10 seconds (depending on fuel tank level) before dribbling. But, there is a way to make my #2 not do that (nor be cold-blooded): turning the tank's petcock to RESERVE position for cold start and waiting a few seconds, then starting, makes all 4 fire right up. After they will run with the choke off, I turn the petcock to normal run position and it is smooth.
I've witnessed this on a few other 750s I have had in my hands for a long period for full restos, etc. I have noticed in those that the late ones (K5/6) with the single-outlet petcock DON'T exhibit this one-carb-sleepy behavior, but the late ones are much more cold-blooded, requiring almost 2 minutes to pull away smartly from a cold start.
I might also mention: having the needles in the middle clip position doesn't match the mix profile for HM341 exhausts, if yours is running those. The middle position is for more-open pipes like 4-1, 4-2 or HM300 series pipes. This controls the mixture starting point where the slide takes control of the mixing from the pilot jet's hole as the pilot loses the suction. With the more-open pipes this vacuum point moves lower in RPM, so raising the needle to the middle matches that well (hence that setting in the K0/1 bikes). With slightly more restrictive pipes, raising the needle a notch brings the slide's fuel into play a little sooner when the backpressure starts slowing the intake speed down, so the velocity over the pilot jet's hole drops and it's suction falls off sooner - quite suddenly, I might add. Having the needle too high for the slide's opening causes sooty plugs, quickly.
And, the pilot jet's feed is what causes the stumble (or lack of it) when its mix ratio is different from that which comes out of the needle jet, especially when cold. Most of the time today, the pilot jet's screw seat is wider than when the carbs were made (because everyone keeps tightening that screw and the carb bodies are soft...), so the "1-turn" setting of OEM days now requires a slightly less-open value to match the OEM mixture ratios. My own carbs run at 3/4 turn now, 150k+ miles and 50+ years later. This provides the most seamless transition when cold, especially, and provides less carbon fouling of the sparkplugs when riding in traffic.
