As for why the Zone isn't a perfect stretch of a circle/sphere, well, the Outposts aren't in a neat circle in this map.
The asteroids that the outposts are constructed inside of are part of a asteroid belt ouside to Rom/Rem's own orbit. There would be an entire circle of about eighty outposts completely around the Romulan star. The neutral zone itself is inside the orbits of the asteroids.
As Rom/Rem orbit during the course of the local year, they continuiously move past the line of outposts, in their larger, slower moving orbits.
The particular outposts attacked just happen to be in conjuction with the two planets at the time of the attack.
This works for me, in fact for many years I've grown closer and closer to thinking of this as the best explanation for what's going on with the Romulans during the 23rd century.
The Federation trounced the Romulans so badly in the 22nd century that they wound up beating them back into the confines of their own star system. Either through a heroic last stand or just the Federation's unwillingness to get stuck in a military quagmire, they stopped short of actually invading
Romulus and instead forced them to accept an armistice in which they were not allowed to venture beyond the limits of their inner solar system. War-weary Romulus spent almost a hundred years fighting civil wars and internal schisms until a new Praetor managed to again unify the entire planet enough that breaking the century-old armistice line finally became a serious possibility.
In that sense, the Enterprise Incident would indicate the Romulans had become a Klingon proxy state in their cold war, in which case their new cloaking device is basically the Star Trek counterpart of the Cuban Missile Crisis (with Romulus being, effective, space cuba
). Years later in TWOK the neutral zone is suddenly mentioned as being the border to KLINGON space, and the academy simulator depicts the neutral zone as a roughly spherical zone of space
that can be circumvented by simply flying around it; yet the location given for it is "Gamma Hydra," same system as in "The Deadly Years." In TUC, we see the Romulan ambassador being inexplicably cozy with the Federation president and also very keen on starting a war between the Federation and the Klingonswhich kinda suggests Romulus was a) not at all a threat to the Federation and b) trying really hard to get out from under the Klingons' thumb. This suggests to me that during most of TOS -- possibly even during Balance of Terror -- Romulus wasn't an independent operator and was actually a subject of the Klingon Empire
So the neutral zone encloses a portion of Romulus' home star system, probably not too far outside of Romulus' actual orbit. I'd also guess that Romulus orbits a smaller member of a triple or quadruple star system in relatively tight orbits, so that the nearest star from Romulus -- the dominant one, maybe -- isn't more than a couple hundred AUs away. Gamma Hydra would be another star on a different orbit that comes close enough to Romulus that at certain times of the year a starship might have to cut through the neutral zone to get to the nearest starbase. The Bird of Prey would be a smaller native-Romulan design, possibly the Romulans' attempt to prove to the Klingons that they could be valuable allies against the Federation despite the fact that they lacked the resources to build advanced warp drives or advanced starships of their own. The mission was evidently successful enough that two years later the Romulans were seen operating Klingon warships, and two decades after that were implied to have a strong Klingon military presence within their system.
Then in TUC, the Klingon Empire falls and they recall their people to the home world to deal with the Praxis Disaster. The Romulans inherit a wealth of technology the Klingons left behind when they pulled out, and in short order proceed to not only break out of the neutral zone but eventually to expand there sphere of influence to enclose a large number of star systems and even manage to force the Federation to promise not to develop cloaking technology; the Narendra, Khitomer systems are either part of Romulus' local star group or close enough that Romulans would have seized them from the Klingons on general principle.
Sorry for the long post, ya'll, but my conclusion is this: the Romulans have always been sneaky and troublesome, but until the years immediately prior to TNG I doubt their "empire" was ever much larger than a single star system. The Bird of Prey may have some of FTL capability via impulse drive or some warp-like propulsion method, but Balance of Terror most likely takes place within a single star system, and that system is the one the Romulans call home.