Cute purse!!
Looked at the video and if you follow her directions I think you will be fine despite the lack of stops. I think I understand your concerns. When you cut the zipper make sure you cut it long enough for the end tab and foldover. Put on the end tab as she describes and if it makes you feel more comfortable sew back and forth a few times at the bottom like I have done on this one .....
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I would not fuss with trying to remove anything from the top - just fold it over as is. Once the top is folded over/down and the facing is sewn to it, the zipper pull will stay put. It will have a small lump where the zipper coil is folded but imho it will not be noticeable . Hope this helps.