Hey man, now keep in mind that I don’t have a damn clue about much so you will have to take what I write with a grain of salt;
Your setup reminds me of mine as far as your right hand goes, and the pick looks like it clears the strings on a downstroke and is trapped in the strings on the upstroke. I would have a pretty neutral hand position so that I could get a good mute on the strings, but I have since embraced my pronation and exaggerated it a bit. Maybe it will help you to do that as well.
That lick isn’t really compatible as strict alternate picking for DSX folks as arranged; it’s 3 notes so it when you start it over it starts on a different stroke, DUD then UDU etc etc
D U D U D U
---------------10------------------10—
—10—12--------10 —12---------
So for me, the most obvious workaround is to place the whole darn thing on a single string if I MUST alternate pick it. Honestly, it’s the string changes that introduce the real picking challenge, so if you just want a quick and dirty solution - remove the string changes! The notes don’t care where they are, as long as they are the right notes and then it’s up to you, the player to ensure that the articulations and inflections sound the way you want.
-----10–12–15—10–12–15
The other thing you could do is not alternate pick everything and simply insert a hammer-on; That buys you time to get your plectrum to the next string.
--------------------10----
------10-H-12----------
Even number of notes works best for us DSX people starting on an upstroke.
Even number of notes is always going to work best for single escape and strict alternate picking situations. Odd note things require either some sort of escape hatch ie legato or hybrid or sweep or DBX or bribery.
I hope that helps, man.