Heichal Menachem comes to mind. They are actually not interested in pushing Chabad but rather in having a shul where people feel comfortable. The only problem is that those who feel comfortable in the HM shul at present are seekers of another kind – very haimish, Chassidish people who no longer feel they want to daven wherever they grew up because of machloikes in their original communities.
I think Airmont (yes, as in Reb Lipa’s Shtibl) is more of a model for what BP needs than either Aish Kodesh or Heichal Menachem. Both AishK and HM are more intellectual in approach; the BP marginal crowd is looking more to feel wanted and to enjoy davening than to have a rov who can really explain things. I’ve only been to HM once and what I saw was a (very mixed as far as origins and affiliation) crowd that was really into heavy-duty learning and therefore just as unattractive to the segment of the BP community that really needs and is crying for guidance than a regular shul would be. Aish Kodesh really isn’t geared to the BP crowd either.
Lipa would choke (literally and figuratively) in the air of BP but there must be someone who can run a shul like that in BP, even if, like Lipa, he lets others handle the rabbonus. The closest shul I know of to what BP probably needs is Rabbi Fund’s minyan in Flatbush.