Recently I've been trying to get into a technique that involves pinky scratch and thumb for 1+3. I'd suggest trying use the meat of your thumb for 1 and the side of the upper joint on 3. I only really use this on rare occasions though, such as when my right hand is busy with other, more invasive things. Best example here would be Ristaccia [a] near the beginning, where it goes from S+1+3+5+7 to the short patterns on 2 4 6 then back to the S+1+3+5+7.
But in most cases, you'd be better off using your right thumb on 3. You said your problem was "moving your hand down" and causing you to miss notes; to that I say don't move your entire hand, just the thumb. Since you have plenty of other fingers on your right hand (I hope) you should be able to continue most patterns just by moving your thumb as opposed to the entire hand.
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