I am definitely of fan of Jerry's mandolin action strumming in the ending of Dew and others such a NFA. A lot of Jerry's lead chord playing like that comes from the top three strings. What I suggest is a combination of two things.
1. Learn every major, minor, and Dominant 7th chord on the top three strings. Triads. A drill I used to do was start out with D. Play D at the open position down at the second fret with the major 3rd (F#) on the first string. Then play D up at the 5th fret with the 5th (A) on the first string. Then play it up at the 10th fret with the root D on the first string. Do the same for D minor, each time playing the next inversion up the fretboard and seeing what chord tones are on each string. When you do it for the Dominant 7th chords, omit the 5th and play Root, 3rd, and b7. After you are done with D, move on to E and so on. What you will find is that having a great vocab in triads on the first three strings will make both lead lines and chord leads happen all over the place. Also, when playing in a band with two guitar players and a keyboard player, music just sounds much better when the guitar players are both not playing Barre chords all the time. Too muddy.
2. Getting a grip on your theory is essential. Most can play the C major scale. However, most can not harmonize this scale with chords. Jerry and Bobby and all the keys players in the Dead were masters with this and is a major reason why their songs have such a strong sense of melody all over the place. There is a lot of theory here involved, too much to write here, but here is the scale in a nutshell.
C Major scale harmonized in chords
I II III IV V VI VII
C maj, D min, E min, F maj, G 7, Am, Bdim
Now take your NFA jam which is tricky for sometimes the jam is in E major pentatonic and sometimes it has a real E mixolydian feel. The difference being the flat 7. Let's say we are playing it in E mixolydian. Plug in the E 7 for the V chord and you can see why Bobby slides a D chord up to E and not a D minor. This song is maybe not the best example for the moods change so much in the jam, which can change the chords of the scales, but I hope this helps. If in fact this just made things more confusing, my bad. My advice is to lay down a groove in A mixolydian, like Dark Star. Then plug in the formula above and play around with some of the chords and you will get a feel for adding chordal harmony.
There are only two mantras. Yum and yuk. Mine's yum.