OK, here are a couple of unrelated (to each other) thoughts:
First, I'm a believer in strict alternation with a pick, with downstrokes on downbeats a la Carol Kaye. (This gets complicated with triplets, but that's another topic.) So, if I'm coming in on the one, it's a downstroke. However, when I'm getting ready to start a line of 16ths (or 8ths at high tempo) I often like to start with a quick pickup note corresponding to the last 16th (or 8th) note of the previous bar, in which case I use an upstroke so I'm using a downstroke on the one of the first full bar. I wonder if some of you who like to start with an upstroke are actually doing this without realizing it (?).
Second, as far as developing the speed and endurance to play those lines, the received wisdom is generally to slow it down to a tempo you can handle, and then gradually increase the speed until you can play the part at tempo. However, another way to accomplish this allows you to practice at tempo from the start, and is the method I prefer. If you're able to play one bar of 16ths at the given tempo without error, start by playing that one bar of 16ths and then "rest" by just playing 8ths or 4ths for the next three bars -- and then repeat. Once you can do this comfortably, move on to playing two bars of 16ths and then resting with two bars of 8ths or 4ths. Etc. The idea behind this is that the problem in playing such lines is not so much speed as it is endurance, which you can build up by giving yourself "breaks" as necessary so your technique doesn't break down.