Great playing! Very tasty.
Yes, stringhopping. Given the way you’re playing currently, it wouldn’t take much to convert this into a pronated crosspicking technique. But you’ll need more pronation / i.e. “upward pickslanting” if you like. How do you know how much is enough? Here’s how I do it:
See the line connecting those two knuckles? Make that perpendicular to your guitar. This will set you up with the pronated arm position necessary for both upward pickslanting and pronated crosspicking. It might feel a little weird at first but give it a bit to sink in. Don’t worry about what the pick is doing, and don’t try to judge whether or not it’s ‘slanted’, per se, even though you might see an upward pickslant. Just look at that side of your hand and try to keep that face of it straight up and down perpendicular with respect to the guitar’s top.
Now, try the four string pattern again, but think about making the movement go side to side, not up and down, not curved. Just left and right of whichever way your arm is pointing. I’d also try three-string patterns since they don’t cover as much distance and you don’t have to worry about tracking as much. Good crosspicking players like Molly Tuttle fly through those.
See if that makes a difference. You’ll know you’re doing it right when the strain you’re describing completely disappears. It will feel like nothing other than side to side wrist movement.