Osprey released a new book, "Imperial Roman Naval Forces 31 BC - AD 500", and this was my first take on 3rd century marines.
Being in the Roman "marines" (the milites classiarii) didn't convey the same prestige as being in the modern US Marine Corps does now. The Roman marines were provincial or foreign auxiliaries that could fight on or off boat. The "milites classiarii" differed from "nautae". Nautae were the ships' specialist crew as well as the seamen who worked the rigging and kept the ship seaworthy. Below the nautae (literally) were the remiges, the rowers, also foreign auxiliaries or Roman freedmen.
Shortcomings:
1) The "santa hats" are the closest I could come to Phrygian caps
2) I need to make the shields more fancy. Playmobil viking shields carry suitable color schemes, but the roman marines appeared to carry oblong shields.
My take:

Osprey's "Imperial Roman Naval Forces 31 BC - AD 500", plate F.

More sources are provided as attachments.
Though the sources depict scenes from the Aeneid and the Odyssey, these were composed in the 3rd and 5th century, and used contemporary styles.