If that is a new engine, it must have a warranty from Honda. If so, you need to contact them and get this sorted out. I can't tell from the picture what is happening, but if you are pushing the speed control all the way forward, across the strong detent so it clicks into the choke position, and the choke isn't closing, then something is wrong. The linkage should snap right forward and touch the choke stop screw. Modifying a brand new engine to make it work is a dumb idea: it needs to be made to work the way Honda intended.
The concern I keep coming back to, is whether you are putting the speed control lever all the way forward past the choke detent. Both the choke and stop positions are relatively difficult to engage - this is done deliberately so you won't kill the engine when you are in the middle of a job. Usually there is a clear marking on the speed control, showing the choke and stop positions at opposite ends. The lever reaches all the way to those positions, if you cross the detents at both ends as you are supposed to.
Last edited by grumpy; 01/04/12 05:53 PM. Reason: Clarify detent issue.