X300 w/Kawasaki starting problem

My x300 has a Kawasaki iTorque twin that will not start unless the choke is full on. Once started, no choke is required and it runs just fine. I can run this thing for a half hour, shut it of and then immediately try to restart it and it won't start unless I give it full choke. Once started, it's fine again.

I cleaned the carburetor thoroughly, and checked the gaskets. I made sure it is all buttoned up nice and mounted on the engine tight with no air or liquid leaks.

I have cleaned dozens of carburetors in my day, but this one is the first I have seen that has a solenoid under the bowl. What is that solenoid for and can it be causing the problem? I guess another question is WHEN is the solenoid supposed to be activated and why?

This is more of a nuisance problem because it works great after starting, I just don't like having to use 2 hands to get it started.

Any thoughts on what might be happening?

Thanks!