I'm going to assume you're wearing the green singlet ...
Your first 5 jumps were the best. You took 6 more jumps after the other 2 guys started vaulting, but there's no worthwhile content in your remaining jumps (or theirs). i.e. You might as well have clipped the vid after the 1st 5.
I don't think your 17.5 flex (which I assume you're on on all 5 jumps) is too soft ... YET. Until you start landing at the far end of the coaches box, you should focus more on technique and less on jacking up the pole flex. That will come later.
On the plus side, your extension is excellent! You shoot off the top of the pole very, very well!
I'm guessing that you're good on the rings and highbar?
On the negative side, you're leaning way too far back in the C. This is most likely caused by taking off under, and by not driving your chest thru (whether you're taking off under or not). To get your posture more upright (so that you can swing quicker and longer), you need to get your hips back, whilst your entire body has a slight forwards lean. But to do that, you need to look back even further - to previous vault parts.
Read thru my reply to Jim in the "Comparing still frames" Video Review thread, and compare your C to Isi's. Once you get that posture, you'll be amazed how much easier your swing will be. THEN move up to bigger poles.
It's good that your coach has ordered you 2 stiffer ones, because as soon as you fix this one flaw, you'll need them quite soon!
I think that Coach Charlie has correctly identified this flaw as well. His advice to "GET BACK EARLIER TO CATCH THE LIFT!!!" is great advice.
The advice I'm giving is HOW to get back earlier. Also, it's not just about "catching" the lift. It's also about putting MORE energy into the pole so that you get more "lift" when it recoils. As a veteran vaulter and coach, I'm sure that Charlie knows that, and has just shortened it. It's a great phrase to use, provided the athlete understands all of the details of what it really means.
I can't see much of your run or plant, but it looks like you might already be leaning back too much thru your plant action. This is one of the hardest things to learn - how to plant the pole while still maintaining a good forwards body lean.
There's a lot of issues and answers related to that, but to pick one typical one, I'd say that vaulters often resist the dropping of the pole (trying to drop it too slowly), rather than letting it drop weightlessly. I'm not saying that that's your specific issue, I'm just saying that that's a common one. I'd have to see more of your run/plant to say more about your specific body actions during the plant.
The next time you take vids, try to get in more of the run and plant. The root cause is in there somewhere, so try to capture it on vid!
I realize that you have the camera on a tripod so it's not easy to pan, but unfortunately, this misses the root cause. If you can't pan, you'd be better off to fixate the camera on your run, plant, takeoff (thru to the C) and skip the rest of your vault. I already know that your extension is sound, and who cares whether you made the bar or not!
Just joking. Actually, I'd like to see the complete vault - including the run and plant. And I'd rather watch no more than your best 2-3 jumps - so that we can focus on improving your BEST technique.
Kirk