First, I do think we should eliminate the term. If it offends even a few people, that is reason enough for me to discontinue the use of the word. It's just a word. If changing it makes someone more welcome at our dances, that's reason enough for me.
Second, what word will replace it? I've heard some of my favorite callers use "walk around." I walk around the block. I don't consider that a dance term. I've heard "dance around," which is slightly better, but still not my first choice.
My term of choice is "Vis-a-Vis, French for "face to face." There is already the precedent of having several French terms:
Do-si-do is "back to back."
Allemande is "by the hand."
Promenade is "walking."
Pousette is "pushcart" or "baby stroller."
When I teach the introductory workshop, I teach the Vis-a-Vis as simply a variance on Do-si-Do. I do not mention eye contact or flirting.
I've started using Vis-a-Vis during my California tour and so far it has been well received and I've had no problems with confusing experienced dancers once the move is explained. It rolls off the tongue very beautifully, and it ends with the "ee" sound, as does the word it replaces.
I hope other callers will give this term a try and let me know how it goes!