The evidence we find of Phoenician burials in the West are typically what we might call "rich" graves, or at least they are graves which seem to have been created with some modicum of care and effort, and they have within them grave goods with indication of value, like lyre-player seals, Greek finewares, Egyptian objects of faience or glass, etc. Some even have Egyptian antiquities from the early Bronze Age. Their activities seem to have been focused on the extraction of resources and not on the acquisition and occupation of territory in the Iron Age (and Aubet and I would disagree on that last point), save for the larger enclaves like the cities of Sardinia, Gadir/Cadiz, Motya on Sicily, and of course Carthage. In most cases it is impossible to differentiate the activities of "Phoenicians" from the Levantine motherland vs "Phoenicians" sailing in and out of these enclaves in the west. In fact, the ceramic evidence (presented by the Germans at the DAE and especially Docter and Niemeyer) indicates that a Carthage-branded version of "Phoenician" red-slip ware very quickly entered circulation in the west in by the end of the 8th century, in a sort of ring between Carthage, Pithekoussai, the Etruscan litoral, Sardinia, Andalusia, and Gadir. We do not have any good indication that the sailors belonged to any specific social class, or even that they represented "public" vs "private" interest. I would argue that the Phoenician evidence in the west supports the notion of a variety of different types of expeditions, with different goals, and with different levels of resources. Some were "state sponsored" like you mention, others were "private" ventures, and some even in cooperation with Greeks, Etruscans, Celt-Iberians, and others (the prime example being the short-lived experiment of collaboration at Pithekoussai).

You've gone astray with the assumption that the Greek sea-faring ventures in this period (the 9th, 8th, and 7th centuries for the Greeks, primarily) were "lower class." When Odysseus is reviled for being a "captain of sailors out for profit" by the Phaeacians in Odyssey, it is not because he is perceived as lower class, but because the source of his wealth and status is presumed to be from mercantile enterprise. This is an attitude which seems to develop in the "Dark Age" of Greece, when land ownership increasingly becomes connected with aristocratic status. So in Athens, we see the development of the idea of autochthonia, and the observance by elite Athenians of tomb cult at old Mycenaean chamber tombs. There is a developing desire to associate elite status with land tenure. This happens at roughly the same time as the formation of polis communities, during which time land occupation become associated with belonging to the in-group. Some scholars argue that the "losers" in this land grab were the old mercantile class, the sea-farers, the merchants, and that we see this developing "anti-trader" attitude in Homer. This would be a shift in what elite status meant, and what qualifications entailed elite status in the Late Geometric / Early Archaic Greek periods, e.g. a shift away from wealth as determined by possession of exotic goods and towards possession of land and its produce within the territories of the emerging Greek states. It is further argued that this "displaced" mercantile elite formed a sort of "mobile population" within the Iron Age Mediterranean which went on all sorts of adventures, and eventually formed the leading edge of the Greek (and to some extent) the Phoenician push west. For the Greek "mobile population," the ultimate solution would then be the foundation of new Greek "colonies" by the end of the 8th century which afforded these displaced elites the chance to acquire land and therefore participate in the emerging re-definition of Greek elite status.

The go-to for this is Robin Osborne's fantastic essay, "Early Greek colonisation? The nature of Greek settlement in the West" in N. Fisher and H. van Wees ed. Archaic Greece: New approaches and New Evidence (London, 1998), p. 251–70.