I don't even bother.
Admittedly, I pick very little... but I just see it as a waste of time picking a muted note like that. Just give it a try NOT sweeping, in fact, on that entire arpeggio (the very first one) I only use the pick three times (when I'm picking at all), others I'll just pick the very first note and just leave the rest up to my left hand.
I can get them pretty fast, 16th triplets at around 150 bpm (just tried), but its not really a 'technique' that I use all that often. Although, I much prefer the way Chris Impellitteri uses it to the way Michael Angelo does, check out http://www.sambob.net/impellitteri.txt
Try to pick as little of it as possible.
