So I went home and played through this and this is what I found. I economy pick or swipe on the transition from the b string to the e string, pick that whole line (no pull off necessary) and back to the b string. The tricky part for me is the same as you, the slide up to the 22nd fret. I found that I can play the lick at tempo if I just play the 22nd fret with my pinky as a four note per string lick. So I play the lick 17 19 20 with my i m r fingers on both strings, then the 17 19 20 22 i m r p and back down. It may not be the way that he plays it, but for my style, it works.
For your picking style, I would practice 17 19 20 on the b, then 17 19 20
on the e. Start with sweeping that transition, like the Joe Stump interview. Just brrrp, brrrp, over and over, to see if you can get to that tempo. I found that I pick differently when playing at top speed, vs trying to learn a lick speed, so I would disregard a metronome and just try to play as fast as you can at first, then slow down to a manageable tempo. Next, chunk the e string lick, 17 19 20 19 17 19 17, can you play that at tempo without the string change? Try a simpler pattern of 17 19 20 19 17 on the e string, then add the two notes at the end. Lastly, play 17 19 20 19 17 on the e, then 20 19 17 19 20 on the b, and repeat that, to get to tempo. That will work the transition back down from the e to the b, seeing that you already worked it going up in the first ‘lesson’. If you want to work on the slide, then I would start on the e string and chunk the 17 19 20 / 22 20 19 / 17 repeat, then add, 17 19 20 / 22 20 19, 22 20 19 on the b string. I should work on that more, as it sounds cool at tempo.