Christopher, it may be time to put the scales away for a bit. As I understand a scale (being a stack of five-twelve notes arranged from low to high) has three basic functions:
1) to serve for technique practice - that is building fluency, speed, uniformity of tone and all that stuff, while working primarily with two or three notes a string.
2) to serve as a pallette of notes to use as the basis for improvised melodies.
3) as a way of creating a decorative texture - for example fast licks in a rock solo.
In terms of 2), this is where it gets problimatic. The use of scales as a basis for solos can be useful, but like you say you have to know which scale goes where. I'm sure John Riley will fill you in on this. However, my feeling is that the best thing you can do to kick of your improvising is to learn how to reproduce the melodies you sing on the guitar. If you can;t think of any melodies copy toehr peoepl's. Make sure they are nice and slow.
This is important, I think, because it stops the process of improvisagtion from being about scales. Don't get me wrong - scales have a use, but if one starts to see scales as something which should be 'applied' in order to produce 'music' you can get into a very academic and intellectual space when you play, which does not interest me. The music is already in you, you just have to let it out.
Having said that, it's good to learn scale theory in order to hear sounds you may not be familiar with.
I think, technically, you will find it very demanding to move onto alternate picking on adjacent strings. Here are some typical sequences that should mess you up nicely. Start off with a slow metronome click (60 bpm is probably the absolute fastest.)
and so on.
Ensure that these notes do not beled into each other - in other words where you cross adjacent strigns on the same fret, you will have to master a way of rolling the fretting finger so that the note is muted before you play the next.
In terms of vocabulary, study your arpeggios. However, make sure that aside from just playing them up and down as exercise you use them to create melodies. Listen to Dave Gilmour's first, major key, solo on Comfortably Numb for an example of this technqiue. It is also use in jazz.
Good luck - hope that's some help!