I was wondering, when you play fast alternate picked runs, how is your right hand positioned?
When I play on the E,B & G strings my palm is rested on the lower strings and when I play on the D,A & E strings it's rested just at the top of the pickguard and I think it's hindering my playing. I try to keep my right hand off the guitar all together but I have a tendency to miss strings when I try to play faster runs.
Have I just not practiced enough unanchored? 'Cause I only recenty stopped anchoring.
Don't play with your pinky on the pickguard. Ideally, your hand should be floating above the strings. When you play with your pinky like that, alternate picking runs that involve all 6 strings become very difficult because switching between high and lower strings involves a position shift. This technique is called anchoring and is frowned upon by most guitar players. You get a lot more freedom of movement if your hand is floating freely above the strings. It takes practice to trust your hand to hit the strings but your speed potential and your ability to reach higher speeds will increase. Playing with you pinky on the pickguard also increases tension, which can cause carpal tunnel syndrome as time goes by.

Resting your palm on the pickguard? That's definitely a no-no.
If im not using the E string, I rest my thumd on the E string and have my fingers hover over the other 5 strings. Ala Jimmy Page
Quote by SForbz-Rockstar

Have I just not practiced enough unanchored? 'Cause I only recenty stopped anchoring.

It takes a while to get used to it, but it's worth the effort.
The key is keep relaxed and make sure your up/down picks travel
very little after picking the string (about 1/2 dist between strings).