1972 CB350K4 Won't Idle

722A carb use a Factory Float height of 26 mm.

Setting the float height is one of the easiest thing to get WRONG.
The TIP of the NEEDLE/SEAT Valve is Spring loaded.
If that tip is compressed at all when you are setting the float height it will be wrong.

The FSM recommend holding the Carb Body at a slight off 90 Deg Angle where the Float Tang just barely dangles down to touch the Needle/Saet Valve Tip.
Getting ther Fuel Height correct in the Float Bowl is a MUST.

The Venturi (Low Pressure effect) draws Fuel UP thru the Emulsifier Tubes.
The Starting Point of the Fuel level within those tubes is a factor in how Lean/Rich the mixture will be.
The higher the fuel level the less low pressure drop is required to pull the fuel up the tubes and vice versa.
The Jets constrict the flow to a maximum amount of fuel that can pass but fuel level determines where in the throttle transistion the mixing occurs

On your Jets:

Right Click on the Pic and OPEN in a NEW Window.
This will give you the factory spec's for your carbs.
Which I belive are:
Primary #68
Secondary #105

If you are running 115 as the Secondary then that may be the cause of your Rich running Black Sooty Plugs.
Did you ever do the Oiling of the Felt Seals?

Also the O-Ring & Washer on the Air Bleed Screw are critical components for a consistant Idle.
They are the ONLY thing controlling Fuel Mixture at Idle.

I do have the original jets as you described them. I may be overthinking this a bit, but I was wondering if it matters which end of the primary and secondary main jets face the bowl. In another thread, I found this response: "I believe the jets have a specific orientation. if you look at the jet, from one side the hole just appears to be straight through, but if you look at the other side, you can see the actual bore of the jet. I think the larger diameter end of the jet is supposed to be the end that is in the bowl, and the smaller end (bore) should be the end that has the o-ring on it and is pushed into the carb...made sense to me, because the larger port would suck up the fuel and the smaller port would help to spray it into the venturi…". Does anyone or agree with this logic? It makes sense to me, and the OEM Honda jets, 68/105, when installed this way, make seeing the jet size (star and all) possible without removing them. Not easy, but the sizes show outside the carb body.

Update: Went ahead and installed 68 and 105 jets with the starred end out side the carb body. Floats set at 26 mm or darn close, maximum of <1 mm off). Plugs had come out with carbon coating, gapped at approx. .024". I think the smallish gap causes inefficient fuel burn and carbon fouling. Pictures of plugs attached.

Cleaned the plugs with dremel wire wheel and 800 grit paper and set gap to 0.031". Fuel/air screws reset to one full turn out (ccw). Bike started w/o choke and settled into 1000 rpm idle. Because previous plugs showed rich mixture, I turned CW both fuel/air screws about 1/8 turn. Idle dropped to about 950 rpm, and used idle screws CW to up the idle to 1200 to 1400 rpm. Bike now revs without hesitation. I'm no expert but so far I like it. Blipping the throttle 4 to 5000 rpm, got no pops or backfires. Bike idled for about 5 minutes fluctuating just a bit between 1300 and 1500 rpm. I'm not sure I followed the correct procedure getting to this point, but it seems to be running much better than February. Can't road test. Comments, suggestions are welcome.

After talking with 66Sprint today, I realized that I may have a blocked idle circuit passage in at least one carb. This diagram is found in a Honda shop manual dated 4/71.

I marked in blue ink the two passages affected by adjusting the fuel/air mixture screw; this is how I understood your description today. I removed the diaphragm, float bowl, primary jet (68), and the fuel/air mixture screw with washer and o-ring, then blew canned compressed air into the F/A mixture port. It came out only where you see the #11, but not out the primary jet passage. I blocked the exit at #11, shot air and then carb cleaner with still nothing coming out through the primary jet passage. I tried looking into the primary passage to see the port to figure out how to clean it. Previous efforts to "clean" the carb included 24 to 48 hour soaks in the Gunk cleaner. Thinking about getting an ultrasonic cleaner. Can you suggest a way to get to the clogged passage?

I'm currently trying to clean the blocked passages marked in the above drawing, without much success. I can only use canned compressed air and carb cleaner, and a very small wire from a cleaning kit. Can anyone suggest how to get at these blocked passages? If an ultrasonic cleaner is the only option, can someone suggest one they have used with good success?

While cleaning, I noticed there are markings on the underside of each carb, in the area normally covered by the float bowl. It's not obvious in these pics, but both carbs have identical markings. In particular, the letter "A" can be seen towards the right side of the carb in the second pic.

The carbs are clearly marked on the outer side 722A. Any thoughts on the marks in the pics? Thanks