1. What is your dowel/rod diameter? It doesn't look like it quite fills the bobbin hole. All things being equal, if the rod fills the bobbin hole it will generate more magnetic pull at the coupler tack. Also, you want the rod to be as high as possible; it looks like it might be a tad below the height of the center-rail? It may be only a 5% effect but every bit helps.
2. Is your dowel steel? The way the rod is bent in your video I wonder if it's some "softer" metal? You need a ferrous rod like steel. Brass, aluminum, etc. are obviously easier to work with but not suitable for the core of an electro-magnet.
3. In your video it sounds (the buzzing) like your working coil is driven by AC. Why are you using DC for the home-built? To be sure, there are good reasons to go DC... just want to be clear what your objectives are before diving into the details of driving a DC coil vs. an AC coil.
4. In the video, you question the need for the bobbin. The plastic bobbin serves no electrical or magnetic function. It is for the convenience of neatly winding the coil. Once the coil is wound, you can remove the bobbin if you can keep the windings in place; not sure how you can do this but perhaps some kind of glue that you drip onto the windings. Different plastics have different heat resistance but I doubt sewing machine bobbins are designed to handle elevated temperatures! 
