"If you don't lift off the 14, the notes will bleed into each other"

i agree and found it hard to play it like that without having to make an awkward change in hand position.
for future referance i also found that fretting the 12 on the Bstring so that the tip of your finger damps the Gstring above to be an easier/more accurate solution to the unwantd pull off note than using the side of your pick thumb.
BTW aiwass, how would you do it, you obviously have a great technique having listened to your link in the general section.