What Richard says is probably the only way to do this. You need to teach your picking hand which new strings start with a downstoke and which ones you have to lift over in order to start with an upstroke. The only way is to start slowly and build it up over time.
Did you have the same problem in Module 10 when we were taught to play the C Major scale in the open position? I know I did. Slowing it down and repetition got me through it.
Without wanting to overcomplicate matters I did see a video of a teacher advising his student to dismiss what his fretting hand is telling his left hand to do and mute the strings whilst picking through a pattern thus isolating the picking hand. That to me seemed over the top but it is harder than you think lol.