Well, since 13 of the 14 founding brothers of Alpha Phi Omega were in social fraternities at the time of the founding (and as far as I know continued activity in those socials) there certainly are opportunities for social greeks to participate.
The wearing of pledge pins and the concept of pledging are similar to what is done by social fraternities. That does not indicate that we are a social fraternity, however at my chapter (Kappa @ Carnegie-Mellon) we did discourage people from pledging a social GLO and APO the same semester (from a simple time management aspect). Pledge one first and then the other, we had brothers who did it in both orders.
I'm not really sure why Centre uses Pillar. Most of the time when changes like that are made its due to pressure from the administration becuase there are no socials on campus, but that doesn't appear to be the case at Centre. It may be appropriate for the section chair to talk to those will hesitations.
Always helps when the appropriate members of the admin are on board, makes the paperwork easier.

I hope the Dir of Vol Activities is willing to be an advisor.
OK, so GIVE isn't a "rival" organization.

Sounds like a ready source of both people who may be interested and community groups who can use service from an Alpha Phi Omega IG/PG/chapter.
YiLFS
Randolph Finder