I’ve realised that whenever I use upward picklaslanting on a guitar with a high action, I brush the lower string (lower in terms of pitch) with my thumb on every downstroke.
Namely, I’ve been practicing a variation on the infamous first Intense Rock lick and found that the picking hand position which allows me to jump from the B-string to the E-string on my nylon-string guitar without swiping the E in the process also makes me involuntarily brush the G-string during downstrokes on the B. Although effective for string change to a higher string without swiping, this hand position leaves the G-string unmuted, so that’s the cause of the ringing; however, if I try to correct that by muting the G with the part of my palm used for palm muting even a tiny bit, I swipe on the downstroke that jumps to the E.
The question is how to avoid the ringing of the G-string as well as swiping during string change? Did any of you experience this issue and if yes, how did you fix it?
I know this was most likely confusing to read, but I haven’t found a way to film myself playing the lick both ways. I’ll do it as soon as I can.
Here’s the video. I’m changing between an slightly ulnarised “extreme” upward pickslant and a less pronounced upward pickslant. I’m not properly warmed up because I grabbed the first chance to have someone else filming me. Unfortunately, you can’t hear the G-string ringing, but it’s definitely there.
Nice playing! Couple things.
First I’m going to answer the question you didn’t ask, and I apologize in advance for doing that!
You can’t play the Paul Gilbert lick with “upward pickslanting”. Technically, an upward pickslanting approach means you can only switch strings when you play a downstroke, because that’s when the pickstroke escapes. And the PG lick requires string changes after both upstrokes and downstrokes.
If you put the YouTube player into 25% speed mode you’ll see what’s really going on when you play this. When you move from the G string to the B string, trace the path of the pick on the screen, and you’ll see it’s moving along a diagonal line. Now trace the path of the pick on the way back, from the B to the G — it’s moving along the inverse diagonal path. In other words, the pick is moving in two different directions. You are using two different wrist motions to make the pick move in these two different directions.
The “slant” of the pick isn’t really changing, and the slant is not causing this change in picking motion either. It is simply your choice to move the hand in two different directions. Moreover, your pick grip doesn’t look particularly “upwardly” slanted to begin with. So… this is why we’ve started looking at picking motions and pickslanting as two different things, so that what is happening will be clearer to you when you’re trying to figure out what you’re doing.
In this case, you are combining two different wrist motions. So this lick, the PG lick, is a mixed motions type of lick, and more complicated than a single-escape lick that only uses downstroke escapes. So, to conclude the question you didn’t ask, to get a better handle on your picking motions, I recommend trying some single-escape licks that use DSX or downstroke escape motion (i.e. string changes only after downstrokes), because that will be easer to do and you can crank the speed on that and really get your motions fluid.
Re: muting, you can’t mute with this technique the way you are doing it here. Muting comes from the center of the palm, not the side of the hand. So don’t expect the higher strings to be muted at all, and you will be happy. If you want to lower your approach angle and place the center of your palm (or at least closer to the center) directly on top of the string you are playing, then you can mute the note you are playing. But you cannot mute higher strings. That’s what left hand muting is for!
Thus concludes the long post you didn’t ask for. 
@Troy
Wow, the man himself responds!
First of all, I’d like to thank you for helping me immensely with my picking technique over the last few years!
As for the 2-way pickslanting and USX and DSX motions, there’s nothing to apologise for. I’m already well aware of that and trying to implement those concepts into my practice and playing in general. I forgot to mention that fact since in this case I didn’t find it to be the source of the issue at hand. Thanks for making me realise that I don’t really have an upward slanted pick grip!
My OCD won’t allow me to have a G-string ringing along with whatever I’m playing on the B-string, so that option is unfortunately out of the question 
I’ve tried to mimic your hand position from this video for the DSX motion part of my lick:
The ringing G-string issue is now solved, but I feel that when making the string change from B to E I have a tendency to slightly curve the trajectory of the USX motion in order to avoid swiping the E; when doing so, I hear that I’m slowing down for the jump from B to E and back to the B compared to the rest of the lick. Do you think it would be possible for me to use the fretting hand to lower the action on the E and allow for a straight-line trajectory of the pick by placing a finger on the single note on the E before making the string change from B to E with the picking hand like this
or would that just make the lick even more complex than it already is?
If the timing is off then the motion is a little wrong. When the pick changes direction there will always be a curve to the motion - only UFOs change direction on a dime! So you don’t have to “do” a curve. The motion doesn’t feel curved, look curved to the naked eye, or really even feel like anything. That’s how you know it’s correct. Just try to do it as smoothly as possible with even time and fast enough that you can’t overthink it.
And try not to spend too much time on this tiny exercise type phrase. There’s only so much you can learn from playing four notes a thousand times. Create longer musical phrases that you would use in a real life situation and work on those. They offer more variety than mini patterns.
Don’t worry about muting. Just lay your fretting fingers on the strings and forget about it. OCD often means doing something incorrectly because you can’t deal with the ragged nature of the way things really come together. Fight that tendency and do the ragged, natural thing.
@Troy
I forgot to mention that the lick I asked about is a chunk of a larger lick in a solo I wrote for one of my band’s songs. I just zeroed in on the last chunk of the alternate picking run since it was the one that I had issues with. This is how it goes:
I think I’m playing the lick here at around 120 bpm, while the lick is supposed to be at 130 bpm, so I’m getting there. I listened to your advice about letting go of the OCD attitude towards my technique and combined my original picking from the first video I posted here for the first two chunks on the D, G and B string with the new picking position I delevoped to counteract the ringing of the G string on the B and E (the second video I posted). This feels natural for me, so I guess it’s alright.
Would you agree that it’s fine to use a combination of different picking hand positions depending on the strings on which I’m playing the lick, or should I develop the same hand position and picking motion across all strings?