I had a similiar problem with my 04, It would only run on one cylinder from closed to about half throttle, and from half up it was good. At first I thought it was a bad plug. But after sticking in a couple new ones it didn't change. After thinking about it I took the left side carb off and there was a tiny piece of dirt that was clogging the pilot jet. I cleaned it out and presto it was fixed.
I think with yours it could be a piece of dirt floating around in your float bowl, and when you hold it wide open it tries to suck that piece of dirt through the main jet and it starves for fuel, and then when you let it sit and idle the dirt floates back to the bottom and it seems fine again.
not sure tho, but I would check there first.