Hey Muris,
I have been practicing few couple weeks now the alternate picking, and i am finaly starting to see good results. I am still not with the speed where i want to be, but my technic is more solid now, so speed is going to have to take some time but the more i practice the faster i get.
What i noticed what helped me was resting my palm on the bridge like you do it, and also lifting up my pinky of pickguard. I play on strat, so before when i leave my pinky on pickguard the volume switch would get in my way, but now when i pick i keep the pinky in the air and so it glides above the volume knob. And its easier to switch from playing palm muted notes to clean notes cuse you palm is right there on the bridge.
Also what i learned from practicing this is metronome is must, and you have to feal and know how triplest, 16th nots etc. sound, you have to feal the rythm of these notes when you pick them, so that you are playing them in perfect time. Triplets have certain feal when they are being pickied as oposed to 16th notes etc.
So i just wanted to share quick update.