Once you are stymied, go back to basics... remove the air filter and make sure both inner bodies of the carb move up and down with the twist of the throttle. Make sure both jet needles move with the carb inner bodies. There's your simple mechanical check.
If you are convinced the problem is fuel delivery because of the appearance of the plugs, that usually indicates clogged pilot jets when poor starting is the symptom. So,... prepare your normal starting proceedure as usual, except twist the throttle to half throttle and kick it over. If it fires, don't release the throttle. If it continues to run at half throttle, but will die when you release the throttle,... it's probably a clogged idle circuit, because you've now established that it wont run in the low rpms, where the idle circuit dominates.
At half throttle the influence of your needle and needle jet interaction, if assembled to spec, has corrected your mixture ratio, so the bike continues to run as long as you hold the throttle open. It's very common for a bike with a clogged idle jet to run at 3500- 4000 rpm, but break up and die at anything below 2000 rpm.
I've had this issue, and my bike had similar symptoms as yours. I eventually drilled out the backside of the amal 930 in question and cleared the idle jet from the back side. then I threaded the hole I drilled and installed a set screw with sealant. I reassembled the carbs after the surgery, and the bike that wouldn't idle or stay running, now happily ran at 1000 rpms... HTH