Hey torpid, again my apologies about getting on my horse, you know 'i have my reasons...
So...
My guitar playing sucks totally... Three years ago, my classical playing was at conservatory entrance level (after playing classical for just 1 year, playing with my nails and everything), but after I took back on piano, I got my wrist troubles, and I quit playing.

Really can't play more than half an hour a week, dropped back to every once in a while, so my playing sucks. And I don't have any recordings of that time...
About the picks... I started with the yellow ones. (Tortex ofcourse, they rule.) Then green, blue. And ended up with the purple ones. A harder pick gives you more control. (Soft picks have something of a faster-than-your-pick-feel.) But you shouldn't really worry about it. Get one of them each, try whichever one suits you best, and you'll notice when you need a harder one.
Vibrato's... I like controlled vibrato's. Not the as fast as you can get stuff. David Gilmour has a good vibrato. Also, you get a more controlled vibrato by moving your finger back and forward in the direction of the string. Might seem obvious for those that know, but on electric guitar, you tend to do vibrato's in the other direction (Like bending). Good for wider vibrations, but much harder to control. On classical guitar, moving in the direction of the string is the only way...
Both tracks you mentionned are me on keys. They're both improvisations. And totally relaxed. Does the 2nd one sound sloppy? Some bad timing but we were all laughing our @ off while playing.
And I do the faces thing too... Heavy breathing all the way.
By the way, my playing is not the cause of my wrist problems. It just makes them come out. The doc told me what it was, but I was half asleep. Forgot...
So, I took my hardest piece up to 20 bpm...
Anyway, I guess the thing is, if you want to learn fast, you have to train hard. When you get it all together, the movements will become natural to you, your muscles will get trained, and it won't take you effort to do what you want. If you try to play relaxed before this point, you will play sloppy.
What you say about the picking hand getting tense, no sync 'till you tighten up your other hand, is normal. If you don't tighten your pick hand, which is, as you know, the way I think you should play, you could get the same speed. Also synchronized. You should have noticed that when playing something you know by heart, technically not that demanding, you play it effortlessly, and it IS played right anyway? That is what I'm talking about. And playing everything this way, even more demanding stuff, will get you there as well. Just another way of working. Maybe not the way to go in rock, but for jazz and classical, this really is the way to go.
On training method I have heard of in this context is rather strange. (And something to get advanced players further after a dead point...)
Just STOP playing, and ONLY do this exercise. start with 5 min a day, just playing 1 note, with 1 finger. Play the same note untill you get it PERFECTLY RIGHT. Then move on to your next finger. After you have done all your fingers, (which could take weeks) try little lines. First 2 notes, then more... Always the same thing. After doing this for a while, you'll give up eventually anyway, but you'll notice that your playing has really improved. Offcourse. Don't try this if you're no advanced player. It helps because doing this, you're focussing on the movement you have to make, doing it the right way. You'll forget about your errors more easily, and blah blah. I never tried it. Not playing is just to much effort... hehe.