Why would it wrong for Nero to discover dilithium deposits on Delta Vega? He was a civilian captain commanding a civilian ship.
If we accept what the Encyclopedia has to say on the
Carolina, this starship was another example of a
Daedalus-class ship in operation in the 2260s. This is more probable with the information from "Conspiracy" (where we have a starship with the registry NCC-42) and the
Bozeman in operation in the 2370s.
From reading the comic, I know that Starfleet visited Phaedus in 2253. April's
Enterprise could have come from this year, or in a year before this year. The jacket he was wearing was worn by Captain Pike in 2255. So, assuming that this jacket came with the uniform change, this might indicate that April served in Starfleet after 2233. So, the time span would 2233 to 2253.