So I did end up lining my Nani IRO Wiksten tunic (with very purple lining fabric). You know, the one that kept crawling up my leggings. The lining makes a huge difference, not just with the embarrassing cling but also improves the drape. It was well worth the effort, even though lining it after it was already made was more of a pain.
I simply cut out another front and back from the pattern in lining fabric, then cut off about .75 inch allowance all around the neck and armholes so it wouldn't show underneath. I also cut off an inch from the hem. After I sewed the front and back together, I finished all the raw edges by zig zagging them with matching thread. Simple simple:
Then to attach it to the inside of the tunic I hand sewed it wrong sides facing just in certain spots: at the shoulder seams, underarms, and two spots close to the hem on the side seams. Voila. I will now shock you with a real life picture of my school room: