It is perhaps unavoidable that different coaches, all trying to help, will have contrasting approaches, which can leave an athlete confused instead of clearly informed. Coach Briggs is a good coach and his drills are fine. But as a Triple Jump club coach who works with everyone from 12 year old beginners up to Olympic Trials qualifiers, I train everyone exactly the same - the Verkoshansky bounding series. While they do the drills, I watch what they are doing wrong and correct their errors, one at a time.
Since I bothered to watch your video several times in slow motion, I was able to identify specifically what you were doing wrong, so that you can work on correcting those things (while you do the Verkoshansky bounding series.) Your video shows that you already understand “the basics on a basic level” so in order to improve, you need to start correcting and improving your mechanics. I suggested the two most obvious things you should work on first.
So just to clarify, driving your arm and knee on your three takeoffs are hardly “advanced techniques.” Examples of advanced techniques would be windmilling your free arm during the hop phase, or using double arm action. KBJT is quite right that you need to be able to perform the critical movements of the triple jump correctly before you start messing around with advanced stuff.