This is something I've been studying recently, and I devised a system of practising to break this down as much as possible. I'm a strict alternate picker, and I noticed that my upstrokes were erratic when changing strings, so I worked out a way to study picking technique across string changes by devising a system of exercises, inspired by drum rudiments. It's not especially musical, and is purely technical, I find that helps me concentrate on pick mechanics rather than getting distracted by harmony. Here's how it works:
These exercises are based around groups of four notes. We have 4 levels of exercises. Level 1 has 1 string change, level 2 has 2, etc.
x means dead string - i begin each exercise using dead strings, muting with my left hand, and study that for a few days until that's really even and I'm comfortable with it before I add notes. I use strict alternate picking throughout these exercises. Play straight 8s to begin with. Swing can come later, that's another ballgame entirely.
Level 1:
--x-x------ ------x-x--
This can be on any pair of strings, and is simply two notes on a string, then two notes on the string above (positionally above ie E>B string). Now, let's go through all the permutations of 4 notes on two strings, going down, including one string change:
-x-------- ----x-x-x
-x-x------ ------x-x-
-x-x-x--- --------x-
And the permutations of moving to the string below (so B>E).
-------x- -x-x-x--
------x-x- -x-x------
----x-x-x- -x--------
Get all of these comfortable before moving on. Do them slowly, with a metronome. Be absolutely precise with the metronome. Are some of these permutations causing you to drag? Then practise it until they don't!
Level 2:
Now we have two string changes, though we never cross more than one string at a time. Permutations going up:
-x-------- ----x----- ------x-x-
-x-------- ---x-x---- --------x-
-x-x----- ------x-- --------x-
Reversed:
---------x- ------x---- -x-x-------
----------x- ----x-x---- -x---------
-------x-x-- ----x------- -x----------
Level 3:
Seeing as now we have 4 notes and three changes, there are only two permutations:
-x-------- ----x----- ------x---- ---------x-
----------x-- --------x---- -----x------- ---x---------
I've probably missed a few permutations, but you get the idea!
Start at level 1, as slow as you need to. I would mute the strings with my left hand and play the guitar like a drum. Forget notes for now, this is just pure technical practice. The more focussed your work, the better the results. I wouldn't advise trying to do the full routine every day, just start with level 1 exercises and move to level two only when you have a grip on it, then you could probably lay off the level 1.
I've been practising this for 20-30 mins a day for 3-4 months. I've seen big improvements in my pick control and ability to play arpeggios across strings!
Later on, add notes. I would often just do one-finger per fret things, like the 'spider' exercise.
Hope this helps!