Some of this is sounding vaguely familiar to a pretty rare thing that can happen in these carbs, which is: plugged or partially-plugged air port to the idle jet. While it's pretty rare, it happened to my own 750 when I was 'down' for over 5 years with cancer and didn't ride it: I did no prep whatsoever, but just ignored the bike for 5+ years afterward. When I started it back up, the plugs in 2 of the cylinders would foul in less than 5 miles, over and over again. After $35 worth of plugs (today this would be over $100 worth!) I pulled off the carbs for the first time since 1980 to go thru them. Cleaning didn't help, mostly because they were already pretty clean. Reinstalling didn't help, either: it ran exactly the same. As soon as it got off idle, it went dead rich, and fouled 3 of the plugs in less than 5 miles, just the same again.
In the end, it turned out to be the tiny air passages that go from the little brass orifice at the back of the air bell, up to the mainjet emulsifier's hole. Two were completely blocked and one was partially blocked, all with the typical white powder found in these carb bodies after the MTBE gasolines etched their surfaces. I pulled the needle jets out to turn them 180 degrees (because they had some wear showing on the downstream side) and noticed a bit of white powder coming out with them, so I ran mechanic's wire down that passage. At first, I couldn't even get thru the passage on 2 of the carbs, while working at it got me thru the third one. Then I worked at it hard in the other 2 carbs until I could run the wire around the bend and up to the emulsifier's tunnel with ease. After reassembly, the bike ran perfectly again. There was considerable amounts of white oxide coming out of the passages, too.
This shows up in the early carbs more than the 657b and later series" probably better pot metal was used in the later ones. I have found it in many of the 657A and K0 carbs that come to me for refurb, but not to the extent mine had.
This all said: the K0 carbs have different emulsifier hole sizes from those found in the K1 and later carbs. The hole sizes are smaller: the early K0 carbs had holes as small as 0.031" for the larger ones. The small ones were the same that they still are, at 0.025". When the cams were changed in the K1 and later bikes the hole size of the larger emulsifiers went up to 0.033" (0.0325" actual, but you probably can't get a drill bit that size...), but this still caused short sparkplug life (like MAYBE 200 miles in city traffic) and we resorted to making the holes bigger (0.035") and lowering the float depths by 1mm for both floats. Keep in mind here: the 657a and earlier carbs have staggered floats, with one being 25mm and the other 26mm deep. If you're using K0 carbs, you'll find they work better with staggered floats. The 25mm side goes toward the bike's kickstand.
Your K0 carbs' idle mix adjust screw's seat is also wider than it was when the manual was written: today the air-fuel mix at 7/8 turn will match what it used to be at 1 turn out, so don't use 1 turn: use 7/8 turn (unless you're at altitude like me: I use 3/4 turn). At 1 turn the sparkplugs will be darker.
My emulsifier holes are also 0.0375: and 0.039" size, with the larger ones being in the middle of the emulsifier's length.
K0 carbs tune somewhat differently from the later versions.
