Just had a quick look at one of your videos (nice playing by the way!), and this is what I do on a 5, but it can be used on a 4 just as well.
If you're playing the E string, try resting your thumb on the pickup. When you go to play the A and D strings, drop your thumb onto the E string - that way, you're muting the E string and when you play the A and D strings, your rest strokes will mute naturally. Do the same thing when you play the D and G strings by dropping your thumb onto the A string - the fleshy part of your plucking hand will mute the E string and you will already have muted the A.
I know that seems a rather drawn out description (hopefully it makes sense?). See how you get on. 🙂