The part is palm muted, so you a resting your picking hand down near the bridge, and yes I do tend to anchor my pinky on the body for stability.

In order to nail this part up to speed with the band, you need to spend lots of time practicing it at a much lower tempo. As a suggestion, start at half speed. If you are still having trouble getting the part cleanly and consistently at half speed -- lower it until you can nail the part 5 times in a row with no mistakes.

Once you've found a slow tempo that you can play the part comfortably ... and this is critical ... keep practicing it at that tempo. The more time you put in at a slower tempo, the more the muscle memory gets locked into your hands and it will be much easier to play the part at faster speeds.

Once you can play the part 10 times in a row at a slow speed with no mistakes, raise the metronome by 5 bpm, and work on it there. Never jump to a faster tempo if you cannot play the part several times in a row without mistakes!

With enough practicing, and inching your way up to tempo, over time and practice it will become easier and easier to nail the part, and eventually, you'll be fast enough to play it along with the band.

Hope this helps! Let me know how it goes!
Mike