I know bringing up whether Romulans having warp drive is like beating a dead targ, but here goes...
In my opinion, the "simple impulse" line was intended to convoy that the Romulan starship was capable of travelling only at sublight, or at most slightly above light speed, at about the same speeds occasional suggested of Star fleet Impulse Engines.
This may actually make some sense in the context of the episode. Since this is the first time the Romulans were introduced.
In this episode, the Romulans don't seem to have a large interstellar, thier empire may very well consist of just the Romulas star system itself. This would make the Romulan neutral zone a sort of "Maginot Line" established by the treaty.
If these outposts are all built into asteroids, its possible that they these asteroids are all part of the same belt surrounding the star system, sort of like the Kuiper's belt surrounding our own star system.
Outpost 2 and 3 are destroyed within an hour of each other, and the attack on outpost 4 (the one we witness) may very well happen an hour after that. This is a reasonable time frame for a sublight Romulan vessel to stage its attacks.
I think the rest of the episode is fairly consistent with this analyses. It doesn't however explain their appearance in Deadly Years. We could say that elderly Spock is just beginning to get a bit senile and forgets for a moment that the Romulans don't have warp drive, but that doesn't explain why the Romulans were able to attack the Enterprise in the first place.
It also doesn't explain anything we see in the 'Enterprise' series, but as with all things in that series I just tell myself "Temporal Cold War" and move on.