The Miko's in Logan Square is also open and delicious. I had some on Saturday.
Mario and Wendee's Italian Ice in Lincoln Park (1136 W. Armitage Ave. 773-327-2885) has a particularly refined chocolate version.
The non-dairy at the place in Roscoe Village is Double Rainbow Soycream from San Fransisco, also available at Trader Joe's (or at least it used to be).
The non-dairy at Sweet Occasions (on Clark) is also pretty delicious and soy based.
Years ago, there was also non dairy ice cream at Soul Vegetarian (205 E 75th St) but I'm not sure they still have it.
I know all of these places are not in your neighborhood, but when I didn't eat dairy, I was willing to travel for frozen treats.