I don't think your stirrups are too short. It's hard to say though just from that picture. It could just be the way the saddle is built or it could be that you are bracing against your stirrups. More pictures or, even better, a video would make it more clear.
I think you would benefit from some work without stirrups, preferably bareback, if you're comfortable with it, practicing just letting gravity pull down through your whole leg and keeping relaxed through your hips. Feel the difference in your muscle tension when you actively try to put your heels down versus when you just relax through your whole leg, ankles and feet included, and just let gravity pull your legs down around the horse's side. Try riding around at different gaits while trying to keep your heels down and then try riding the same gaits with your legs hanging like the girl in this photo. Even try riding around with your toes pointed down Take note of the differences you feel. Which feels more balanced and secure for you?
Another thing to notice, with your feet out of the stirrup or bareback, how far can you put your heels down? Have someone take a picture of your leg like that, so you can see it. That's really as low as your heels every need to be. If your heels are much further down than that with stirrups, that's a pretty good indication that you are bracing in order to achieve that, since you can't do it without the stirrup. There is nothing advantageous to having your heels down drastically, versus just slightly. The important thing, is just allowing everything to be relaxed so as to absorb shock. Just as you saw in the video of Charlotte Dujardin, her heels really aren't down much at all, and it certainly isn't a detriment to her riding :)
I ride cowhorses, and we typically ride shorter stirrups than other disciplines, because you do need your stirrups to help stay balanced for the very quick maneuvers that happen on a cow. If you're reaching for your stirrups, it's a lot easier to lose one when things get faster. But, yes, my stirrups are too short in both those pictures I posted and in the one, the saddle is too small for me as well, which further contributes to making it hard for me to have a proper seat.
Here's a picture from the same ride that the first picture I posted is from. Even though the stirrups are short, I am still able to stay balanced and centered while spinning pretty quickly. It probably wasn't as easy (or as pretty) as it would've been with stirrups a little longer, but I don't remember having any problems. If you can keep your muscles relaxed, you can work around improperly fitting saddles, too short stirrups, rough riding horses, wild bronc rides, etc.
I didn't work a cow that day, so I can't say how I would've fared through that, but I do some sliding stops without issue.
But the short stirrups are the reason my heel is so exaggeratedly down in the pictures from that ride. And my ankles were pretty sore before too long.
Just keep working on it! Equitation is a constant battle we all have to deal with. It sounds like you are having success playing around with some different techniques. So long as you're making an effort to improve, it will get better/easier!!
I wish I had a before picture easily handy, so I could show you how terrible my equitation was a year ago, before I started really working on it. At the time, I knew it wasn't good, but I didn't know why. I needed someone to point out to me, exactly what needed to change. I'm far from perfect, but I'm a bajillion times better than I was! And, amazingly, I haven't fallen off nearly as much as I used to, when I was riding with terrible eq!!