When you lift the pistons up by hand and let go, do they drop down immediately or do the slowly fall? They should slowly fall. The exact rate isn't important, but it should take a couple of second for them to come back down.
If the fall immediately, there is an air leak above the diaphragm which is not allowing any vacuum to develop. You may have a timing related problem in some measure, but it look like classic "lean" to me. The needle isn't withdrawing out of the emulsion tube so you aren't drawing near enough fuel through the jet.
It's going to run somewhat lean without air filters, but it should run OK. You need to get those pistons working. As you surmised, something isn't right.
- You don't have idle air screws. These carbs control the idle mixture by varying the fuel, not the air. Yes, the O-rings are important.
Also, with all due respect, you have no idea whether your carbs are clean until you see streams of carb cleaner spraying out every orifice in the carb. How do I know? Mine took 5 cleanings including 2 boils and I would have sworn it was perfectly clean every time. However, having sprayed carb cleaner through every hole in the carb and personally having seen the unrestricted spray of cleaner out the other end of every passage, now I know.....and the fact that my bike has run pretty near perfect for 2 years confirms.
The picture below has the idle mixture on the bottom rather than top, but you get the idea.