My 2 cents- There's a setup problem with your choke linkage. I say this because there are 3 separate carbs but the common to all three is the linkage. If you had reported that it would fire on 2 or 4 cylinders and then the rest would eventually fire up, then I would suspect faulty (blocked) choke circuits. Something is causing the choke plungers to not open up enough to provide the enrichened fuel mixture. In a slimplified explanation, the choke circuit on these carbs is a little mini carb with rich jets. You either open them up or they are closed On a majority of "other" carbs, there's a butterfly valve that closes down the main throttle bore which causes higher vacuum on the main and idle jets richening the mixture. Keihin have always gone with the choke plunger type.
The other thing that can happen in situations as you''ve described, is too much air flow through the throttle bores which will starve the air going to the choke circuit. This could happen if the idle circuit has issues and in order to keep the bike running at idle, the throttle plates are open more than they should be.
The reason the hair dryer trick works supports the reason we have choke circuits in carburetors. Cool/cold air and cold fuel will not mix properly and the only way we can get this cold mixture to combust is to give it soo much gas and hope that some of it ignites. Once the air intake runners and the carb bodies start to heat up along with the cylinder walls and combustion chamber then the fuel mixture will heat up and homogenize and then total combustion can happen.
One test you could do to confirm the problem in the choke circuit is to get the engine up to running temperature and then with the engine at idle, open the choke circuit full open . If it doesn't flood, studder and almost die, then you know the choke circuit is the problem.
Last thing that comes to mind is the fuel source for the choke circuit. As I remember it ( and it has been a couple of years ince I delved into the carbs) is the fuel pick up point for the choke circuit comes from a port in the bottom of the float bowl and up through an enrichment tube in carb body. See this post Of my rebuild specifically post #6097.
www.kz1300.com/index.php/forum/carburato...carb-issues?start=12 I found the port in the float bowl blocked with crud which I believe is caused by the ethanol in the fuel, mixing with water and settling in the bottom of the float bowls and then the aluminum in the float bowls oxidizing causing the white powder like build up. In this post you can also see the whitish residue on the choke circuit fuel pick up tube/jet.