And for that matter, the Needle too, since you're in 6a.
If I was anywhere colder than 7a, I would chicken out and only plant a Needle south facing. I would not experiment with north facing.
But to be honest, I wouldn't plant palms at all in 6b or colder. And in 6b or colder, it's actually hard to find good, leafy BLEs of any kind. 7a is really the zone where your BLE choices widen up. I'm talking things like cherry laurels, photinias, aucubas, magnolias, camellias, and so forth.
With a few leafy BLEs, a couple of hardy yuccas, and some creativity, you can create a very "tropical" looking outdoor space in the Middle Atlantic.
Re: Sabal Birmigham hardiness
I can only tell you my experience. All palms were planted in 2007. So, this is with a dozen years experience.
Because I planted the Birminghan in front of a church business office, I could not burlap wrap it or stick a trashcan over it for winter. It would be too unsightly and give off a bad vibe. So, all it gets every year is a pretty big mound of mulch. It is sited against a granite east-facing wall. The soil profile is most unusual. The top 6 inches or so is tan colored clay. Under that is a couple of feet of sand! The result is a very fast draining soil, but also very easy for the roots to penetrate. In terms of winter damage, the palm has defoliated completely, except the spear, on maybe 2 (out of 12) occasions. My Minors, by comparison, have defoliated (except the spear) 4 or 5 years. Additionally, when the Birmingham isn't defoliated, it hardly damages at all, except maybe a few white "pin holes" which it is susceptible to. So, it's either all or nothing. The regular Minors can show all kinds of intermediate damage. As sort of a rough guesstimate, my Minors go undamaged a third of the winters, get severely damaged a third of the winters, and get moderately damaged the remaining third. They've never lost a spear, though, and always recover. In contrast, the Birmingham gets severely damaged 1/6th of the winters, and only superficially damaged/not damaged at all 5/6ths of the time.