The concept of a single-system Romulan Empire is really attractive and works within the initial episode, Balance of Terror. The name of the war, the "Earth-Romulan conflict" also makes sense, since it was one solar system vs another (albeit with some allies here and there). No need to try and explain this away in terms of the Federation.
Unfortunately, that is where the theory runs out of good ground. Every later encounter seems to refute the notion - Commodore Stocker takes a "short cut" across the NZ to reach Starbase 10, an absurd concept (in interstellar terms) if the RNZ merely surrounds a single star - you are effectively cutting through a solar system! Season 3 episodes have the Enterprise actually crossing to the other side of the RNZ, in one instance getting almost instantly surrounded by enemy vessels, in another spending several hours on a hitherto uncharted planet.
Instead, I'd like to concentrate on the one piece of visual evidence we have for the Romulan Neutral Zone:
I believe the one thing the star chart establishes beyond doubt is that we are looking at Sector Z-6 and its quadrants (reminder: in TOS a quadrant was a smaller piece of a sector!).
But I'm afraid the information on quadrants we can get from TOS is not sufficient to establish a reliable sense of scale.
The question remains what happened after events in "Balance of Terror". I somehow find it hard to believe that the Federation did not contact the Romulans via subspace radio to tell them "We know it was you, we've got the evidence, and any furher incursions will be dealt in a manner as we see fit."
Especially, after one (warp-drive capable) Romulan ships had made it to Tau Ceti (11 light years from Earth) and was defeated by the Enterprise
according to "Whom Gods Destroy".
This may have resulted in a dialogue and Romulan bartering to renegotiate the treaty, i.e. expending their territory beyond the Neutral Zone we saw on the star chart.
It's interesting to see that our protagonists both in "The Deadly Years" and "The Enterprise Incident" are eager to keep the (new?) treaty, although it's crystal clear that the Romulans violated the (original?) treaty in BT.
As Mytran just added, someone else attacking the outposts on the Federation side of space could have deliberately done so to start a new war with the Romulans.
Thus Kirk had to give them the benefit of a doubt, as it appears that such actions aren't entirely without historic precedent