I understand I am a little late to this game now. but here is a list I made up, and posted on my blog of things to check before starting carb adjustment. The tech specs part is for the cb360...So, they may not be correct for your 350. double check your manual.
Getting ready to tune Keihins 754 on the 76 Honda cb360
Carbs can not be clean enough, clean them. Clean tank and fuel tap. Gas cap venting properly?
1 are your carb diaphragms new? It sucks to tear an old one halfway through this process. like I did. New diaphragms available here. http://jbmindustries.com/
2 do you have the original stock Keihin air/fuel adjustment needle springs installed (BEST) OR Did you file sharp edges off new carb rebuild kit air / fuel adjuster springs ? link to more info on my blog.http://www.hondabrat.com/2012/05/kehein-754-carbsso-close.html
3 Do you have in line fuel filters or screens on fuel tap? clean tank ? vented gas cap?
4 Do you have good stock coils or new coils ? good condenser ?
5 Good plugs set proper gap (.7 - .8 mm), NGK B8ES, (NOT NGK BR8ES) and 5 or 10 ohm plug caps ? I have 10 ohm (pjs recommendation w stock coils) works great.
6 Timing set properly w timing light ? good points ? properly adjusted .3 - .4 mm gap
7 cam chain adjusted properly ? trap crank w wrench while setting cam adjustment bolt.
8 Valves adjusted properly?
9 Rubber carb insulator boots and gaskets in good shape (no cracks or leaks). Best price I found for New boots and gaskets is my local Honda shop.
10 carbs properly synchronized w gauges?
11 throttle cables properly adjusted and lubricated?
12 Ensure fuel lines/filters do not contact engine, engine mounts or frame.
13 make sure carbs are level to engine.
14 Tank or tap not getting hot. From what Ive read online, the boiling point of most gasolines is 90 - 400 degrees F
Is there anything else forgot ?
It would take a big day to check all this...but it would only take a day. and its a great place to be sitting when getting started on carbs. Because if something is not right it can produce false plug readings.