"Struggle-ups" are a real good description of what I've managed to do for a muscle up. Usually I manage to get one elbow up in the air above the bar and one elbow down (which is a terrible boob-smasher, btw), and then a good hefty kip and I can get all the way up. The next step will be to switch which arm is up and which is down, and then, eventually, to getting both arms up evenly. In your case, working on dips and pullups will definitely help, and I strongly second Brandee's comment about kipping. My only comment would be, rather than the dip machine, do you have access to parallel bars, or, better yet, rings? They can help strengthen a lot of the stability and control muscles of the shoulder than will help you get over the bar.
Fortunately I have the muscles of the shoulders well developed and strong
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