First, the problem: Try changing the oil if this problem bothers you enough. I wait 2500 miles and at about that time, I will notice the bike miss a shift now and then. That's the real signal to change oil.
Before the oil needs changing, it's not uncommon for me to have the same problem you are experiencing. Come to a stop sign, I only got down to 2nd gear before stopping, the transmission won't go from 2 to 1, it gets stuck between 2nd and first but not in Neutral, the gear indicator goes blank. Slowly, carefully release tension on the clutch lever until it pops into 1st on its own and then pull the lever back to the grip. Another thing that might work is to roll the bike a few inches but that takes more work.
Thanks for reminding me to check the mileage on that oil I'm running now.
Second, Chinazzos: There was a great thread going here years back about counterfeit Pazzos. A guy did a test with lab equipment. He didn't want to put an expensive Pazzo through the same test but he determined that even though the metal may have been inferior, the Chinese copies were probably at least as strong as real Pazzos. The Chinazzos I bought were a bit paler in color than real Pazzos. They were also a bit thicker than real Pazzos which may have been an improvement. I've noticed in a few cases where I bought Chinese knockffs, the parts were not only copied but the design was improved upon. There are probably many factories in China that copy Pazzos so some might not be as good as others. The anodizing is likely to be inferior in appearance and it may fade easier. So far, I've had good luck with Chinese parts. I've bought three sets of Chinese axle sliders over the course of a few years and it appeared that the design had been improved each time. They're not just copying, they're innovating. Chinese parts are often worth a try considering how cheap they are if you can wait a few months for delivery. Bear in mind, it's probably never worth return shipping if you are not happy.
I have Pazzos on both my bikes and as long as they are installed correctly, they work great. The Suzuki has a better mechanism than Kawasaki for interfacing with the master cylinder so improper installation would be unlikely on a busa. I have heard of the levers putting pressure on the MC resulting in the brake switch constantly being activated or the clutch slipping. If this were to be the case with your Chinese clutch lever, the clutch would never be fully engaged. Engaging it more by releasing the lever halfway wouldn't cause the shift drum to roll easier than completely disengaging the clutch by pulling to the grip.
I would first change oil. Not instantly better? Change the Pazzo copy to OEM and test it. Buy an OEM lever on Ebay if necessary. I think your problem is worn out oil though.
...and don't put your bike in N at a stoplight! That's unnecessary risk. Leave it in 1st.