The helots were not a fetter particular to Sparta; everyone else had slaves to keep down, after all. Nor was a lack of people surviving to reproduce a problem either. Rather, the core weakness of the Spartan state was the system of divisible inheritance, which made it difficult for many families to keep their Spartiate status. Even then, it's hard to say how much a lack of full citizens actually hurt them; the vast bulk of their armies had always been made up of their allies and the lower class Lakedaemonians, and under Spartan leadership, they were just as effective in combat.
In terms of the limits of Spartan power, permanently humbling Argos and Achaea and forcing them into the Peloponnesian League would be a good start. Unlike Athens, they don't have quite the wealth and access to international markets to shrug off large scale destruction of their harvests, so a Spartan led invasion could inflict some serious damage. The main problem is that Persia is so powerful and wealthy; if Sparta becomes powerful enough to be a threat to their Western provinces, they have essentially unlimited money to throw at their Greek enemies. Ionia and Cyprus are thus permanently outside their reach, barring the collapse of the Achaemenids. However, the Persians were willing to support Spartan hegemony over basically all of Greece south of Thessaly, though maintaining that is tricky. If the situation in mainland Greece is stable, Sparta can move to enhance their position in Sicily, sending a drip feed of experienced officers (plus mercenaries, helots, allies etc) to lead the armies of whichever Sicilian city they want to see grow in power.