That is how I got April to stand still while mounting as well. The difference is that I really made April work on the lunge... no troting for her!!! April would either buck or rear when I would get the halfway on point- but now she stands perfectly for a mounting block... I would def. Recommend this technique.
When I first started working with April it took over 45 minutes to get on one day. After she just stood I walked around and dismounted and that was the lesson. The next ride it was like 5 minutes. As soon as she moved and then I made her lunge it was like "ok I get it"
I have to say, I strongly dislike how the lunge line is clipped to the bit. In the video, you can see how unbalanced the mare is because she's getting yanked in the mouth and just swinging her hind end out everytime her nose gets pulled in. That's a pretty good way to make her mouth sore and leery of lunging, especially if she decides to throw a fit and is having the bit yanked through her mouth.
I never longe with a bit...it's easier to just slip a halter on over the bridle for ground work prior to riding, even something like this. As far as the reins, for the most part, when I'm riding at home, I use cotton reins, that have clips on the end, so if I'm doing ground work before I ride, I just un snap, and tie them up and hang them over my horn. It might be an extra step when I stop the horse, and prepare to mount, but I'd rather have to reclip them back on then risk the horse getting caught in them. However, I have different methods that I use to train a horse to stand still to be mounted anyway, although moving his feet is part of it.
I read this earlier and thought I might give it a try on the horse I ride. He's had a week off, which usually makes him a bit hot and ready to go. Normally he won't stand for me at a mounting block, he's off the moment your butt hits the seat and dances around when I tack him up. I did it in a roundpen so I didn't have to worry about halters and lunge lines at all.
I've got to say, it worked great. It took all of working circles twice to have him standing steady to be tacked up and twice more to get him steady and still during and after mounting. I got off and remounted at the end of our time and he stood very well again. He also wasn't at all hot today, much to my surprise. Maybe turning his brain on and letting him make the choice that working with me was the easier option from the start helped!