Yeah, arpeggios are where it's at, especially when learning this stuff. You seem to know your answer, but just haven't applied it yet. And you'll take forever to get there if you're trying to learn "at full speed" during a song. :) To learn this stuff you really need to stop and think about it, rather than just hope it all comes together on the fly. Once you know what you want to do you can practice it during songs.

You might wanna take something simple first, without too many changes. Take the first chord and learn its arpeggio in at least two or three positions. Figure out a few little licks to experiment with. Now play your backing track and, ignoring all the other chords in the progression, play around with your arpeggio runs for this first chord. Rinse and repeat. Then do the next chord on its own. Then do them both. You get the idea, eh?

Do all this with modes as well, even with the modes that don't make any theoretical sense played against your chords. Everything can be useful in a certain context.

Something else you'll want to look into is substituting chords (and thus scales and arpeggios). But you say your theory knowledge is superb, so I won't bother you with details about this. ;)