Please note this is something of a legacy page and will be updated with new information in due time.
It is worth considering an admittedly late source, a list of "thalassocracies" preserved in Eusebius' Chronicon and originally appearing in Diodorus Siculus. The list, which was extensively studied by Molly Miller in the 1970s, claims to emend the names of powers with a seaborne hegemony along with the period during which the state exercised that power. The Phocaeans and Samians - both credited with far-flung feats of exploration and colonisation - are both mentioned as exercising thalassocratic power during the 5th century.
The list presents information dating between the Trojan War & Xerxes' expedition to Greece in 480 BC. The material for the latter centuries is as follows: -
Perhaps the Lesbian thalassocracy can be associated with the career of Pittacus. Pittacus killed Phrynon of Athens in single combat. Again, the chronology is problematic: Eusebius associates Phrynon with the 36th Olympiad [i.e. 636 BC], whilst Diogenes Laërtius has him as a contemporary of Croesus [1.75-76], despite flourishing in the 42nd [612 BC] and dying in the 52nd Olympiads [572 BC] [1.79]. Michael Grant tentatively places his decade in power from c.590 BC, fitting with the era of Periander, who arbitrated between Mitylene and Athens. The Lesbian thalassocracy was preceded by three of indeterminite length, probably the Carians, with the Milesians before them (likely under the tyrant Thrasybulus), themselves following the Egyptians. An Egyptian thalassocracy would almost certainly be associated with the reign of Necho II, though this is even more problematic, as his reign straddled the turn of the 6th century.
With regards to the Samian thalassocracy and its juxtaposition with that of the Lacedaemonians, this passage would reflect the career of Polycrates, the tyrant of the island between c.535 and 522 BC, who was opposed by the Spartans [Herodotus9 3.44-47]. The succeeding Naxian domination could be connected with the tyrant Lygdamis, though Herodotus [1.61, 1.64] makes this figure a contemporary of Pisistratus of Athens, thus a mid-6th century figure. Dimitar D. Mitov, in his analysis of Miller's work, notes that Thucydides also provides a succession of thalassocracies [1.4; 1.7-8; 1.12-14], though, despite some similarities and Thucydides relative chronological proximity the events in comparison with the later writers, the two do not always tally: -
As such, there may be historical value in this list but it is subject to so much compression as to be unable to shed any light on the Phocian and Samian expeditions to Tartessus.