I wouldn't focus on going faster just yet, you already look a little bit flustered through the course. It's a little difficult to critique, with the angles, but the second jump you look like you got a little left behind? I'd work on your two point a little bit more, you just seemed very tense through your hips, very upright through your body and looked like you caught your horse in the mouth with very little release. You were leaning through your turn to the third jump, which threw your horse off balance, thus making it harder to get up the right amount of speed / power, you also seemed to get left behind over that jump, the last one looked good.
Remember, you're more likely to knock a pole just racing around the course, jump offs are NOT so much about galloping, but more about the way you use your space. Yes, you do need to move faster but that's only one part of it.
So I just watched the video again and I definitely have to say you need to work on your release. It doesn't look like you give much of a release over any of the jumps, instead you stick your elbows out to the sides. You need to be following your horse with your hands, focus on really moving them forward with the motion of your horse.