I thought it might be even more twelve-y to start this new movement in 12/8, so it does indeed begin with the 12 notes of the row split up equally amongst all four instruments in a 12/8 bar. (I've dispensed with alto clef below so as not to confuse any violists.)
[Yes, I know there are parallel fifths between soprano/bass.]
When I created this row (to go with the oh-so-serioso words "When Jesus Wept..." as described here) I hadn't noticed that the wraparound notes 12, 1, and 2 create a C Major triad, but it suddenly seemed very lighthearted to have a 12-tone piece break into this simplest of keys, especially given Schoenberg's famous quote, "There is still plenty of good music to be written in C Major." Plus, to be honest, I'd been struggling to summon a jolly mood sticking strictly to 12-tone ways. So the die was cast: this movement would be aggressively tonal comic relief, while still using the row as a basic building block.
The rest took shape pretty quickly, although I still consider this very much a work-in-progress. It has a basic ABAB structure in which the trio-like B section is darker and features the primary row as an extended lyrical melody (mm.26-42) passed among the upper three instruments. The B section is introduced by the most stridently 12-tone harmonies in mm.24-25 (and later, mm.69-70) in which the 12 pitches of the row are deployed across three successive chords. Otherwise, the row is used in a much breezier manner, with the "accidentals" functioning more as chromatic decoration than tonal disruptions.
The 12/8 meter led pretty naturally to a fiddly jig tune, and though the bass line is quite primitive most of the time, there's a sort of funhouse passage starting at m.54 in which the cellist suddenly plays the row in retrograde; for three bars, all four parts are cranking out versions of the row, but things snap back into place just as quickly, the exception having proved the tonal rule.
The recording is again, of course, played by horribly unsatisfying virtual string players (especially in the more lyrical parts) so one has to use one's imagination, but if there's one thing I can say for this piece...it's short.
The strongly contrasting "first" movement, in case you missed it:
P.S. Did I consider titling this post "A Phony Thing Happened on the Way to the Dodecaphony?" Yes, yes I did. I've also realized that my instinct is always to spell Dodecaphony as Dodecacophony (as in dode-cacophony).