I'm trying to learn the main riff to The Red Hot Chili Pepper's "Sikamikanico". According to tabs I've found on this site it is basically:

G --0-0-0-3-0-0-0-3-0-0-3-0-0-3-5
D --0-0-0-3-0-0-0-3-0-0-3-0-0-3-5


It's played pretty fast and is practically tremolo picking but not quite that fast. I'm having trouble picking that fast on two strings at once, mainly when hitting the two open strings. Also, how do I mute the other 4 strings during this part? I've got my thumb over the low E and A, but I need my other fingers in position to play the notes on the third fret so they can't be muting the B and high e strings from ringing out.

If anyone has any tips for playing this riff please let me know!
I've seen 2 famous guitarists tremolo picking 2 strings differently.

Steve Vai uses his wrist but imagine really moving your wrist from side to side as if you're shaking it.

Rusty Cooley also does it but he uses his elbow, I don't think it's as safe but it looks far more controlled and if you need to speed up this way helps a lot more.

Look up some videos and you'll see what I mean
In order to correctly finger and mute this riff:

-Mute the low E and the A string with your picking hand

-Fret the G and the D with with your index and middle finger. It doesn't really matter which of the two is on which fret, find out what's comfortable for you. For extra muting, make sure to use the tip of the finger fretting the D string to mute the A string.

-Mute the remaining B and high E with the aforementioned fretting fingers

As for actually playing the riff:

-Play from your wrist. I myself achieve quite similar results to what I'm hearing by using the same alternate picking motions that I would normally use on a single string, but then made a little wider in order to pick both strings. I really wouldn't recommend using the elbow.
I didn't think to mute the lower strings with my picking hand. This actually puts my wrist in a better position to strum at this speed as well. Thank you for the suggestion!