I've answered my own question. Just back from Jerusalem, and, based on reco's from locals, found Abu Chukri in the heart of the Old City. It's at the intersection of Al Wad and the Via Dolorosa -- across from the 8th Station of the Cross.
Absolutely terrific hummus, schwarma, etc. So authentic, they had to hunt up someone on-staff who spoke English. And, the _BEST_ pita bread I've ever had -- a little fluffy, and warm from the oven.
Wound up eating there 3 times over the course of a week. Don't miss it....