That’s not always necessary. You can rest on the E string while plucking the D string, because your plucking fingers are going to automatically mute the A string anyway.
It all depends on the sequence of notes you’re playing. If it’s a lot of jumping between A and D, then rest on the E string. If it’s just A string, then rest on pickup or E.
I think you just need more practice. I created a thread a while back with a bunch of exercises/warmups, there’s plenty of string crossing and skipping there. Take a look, maybe some of them would help you too.