When cross picking, is it OK to down pick as you go down toward the first string and up pick when going toward the sixth string, or should I be following the down-up picking rules?
Cross picking question
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Copybook style is down-up, down-up. But you can make up your own style if it suits you and if it does not compromise on quality and speed. My two cents…
Alternate picking rules don’t depend on what strings you’re playing, but rather what beats the pickstrokes land on.
Here’s the simplest way I explain it to students: count “1, 2, 3, 4” at a steady tempo. Play only downstrokes on all of those numbered beats.
Then count “1 and 2 and 3 and 4 and”, at the same tempo (but now with twice as many beats in the same amount of time.) Play D-U-D-U-D-U-D-U.
All of the numbered beats (1, 2, 3, and 4) remain downstrokes when you play them; nothing’s changed about them. But all of the “ands” should always be upstrokes. They land in the “spaces” between the downs.
Learning alternate pick directions is essentially learning to always play downstrokes on the “number” beats and always play upstrokes on the “and” beats, no matter what other factors (left hand ornaments, string crossings, syncopated rhythms, etc) are there to confuse you. 
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I agree with what Michael said, but I would like to note a few exceptions, and why you should or shouldn’t bother about them.
Several well respected flatpickers, most notably Tony Rice, would use either a D-D-U or D-U-U crosspicking pattern. If you are an advanced player trying to accurately mimic Tony (or Jesse McReynolds was another who played that way), Then you should think about using one of those patterns. But even with either of those, it is a consistent pattern.
If, on the other hand, you are a beginner trying to develop good technique, (which I would assume is the case, based on the question) Michael’s advice is spot on. You need to learn the rules before you can think about breaking them. I hope that wasn’t too confusing
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Thank you all! I appreciate the input, and I’ll get to work on this!