Once warmed up, bike idles fine? Only three things needed for combustion: spark, air and petrol. Spark is fixed by crank-rotation. If you're getting combustion, spark is working. Air is dictated by throttle-plate opening. Should set only once and leave it. Petrol-flow is controlled by numerous carb circuits. Since you have to fiddle with it so much, sure sign carb needs deep restoration.
I got my 2009 street bike with 8000-miles on clocks. It had been sitting for a year after owner crashed in parking-lot and decided to hang things up for good. Was saving it for his son, but kid wanted Camaro when he turned 16.
Bike was difficult to start. Especially when cold and I'd have to fiddle with all the levers and knobs like yours. I thought I "cleaned" it well enough with spray carb-cleaner, hah! I had done maybe 5% of job. Your carbs need more thorough cleaning.
Many great mechanics. Who can remove engine in less than 15-minutes. Who can rebuilt engines in less than day. Have had to remove their carbs 4-5x for ever deeper cleaning before their bikes ran great. I suggest you do it 1st time around. Well, 2nd time now.
Here's some photos of what's involved. Need to scrub out all hidden secret passages in carb-body.
https://www.ninjette.org/forums/show...87#post1267487
Some related threads:
https://www.ninjette.org/forums/showthread.php?t=330960
https://www.ninjette.org/forums/showthread.php?t=322846
https://www.ninjette.org/forums/showthread.php?t=321223
https://www.ninjette.org/forums/showthread.php?t=317977
https://www.ninjette.org/forums/showthread.php?t=317810
https://www.ninjette.org/forums/showthread.php?t=316395
https://www.ninjette.org/forums/showthread.php?t=315193
In end, I sent carbs off to ducatiman for refurb and restoration. I didn't want to buy all equipment needed (scrub-brushes, ultrasonic cleaner and micro soda-blaster). Or spend decades learning how to restore carbs back to factory-fresh clean.
Carbs came back perfect and bike ran like brand-new like off showroom floor! Also send in petcock, it most likely needs rebuild. Last January was perfect test as it had gotten down to 27F. I wanted to go for ride before heading off to Hong Kong for 3-week vacation. Just pulled choke to full, didn't touch throttle or anything and pushed start-button. >VRROOMM!< It started on first crank and settled down to smooth idle. Was ready to ride by time I got helmet and heated-gloves on.