Have I overlooked Qart-Hadast all this time?

[Lysimachos]

The Karchedoi indeed have a very versatile unit roster. You are right about the almost identical stats of the units you mentioned to the hellenic variations (I think the Hoplites and Thureophoroi have 2 points higher morale). They have excellent units for practically any purpose, including assault infantry and phalanxes. Perhaps the balearic light infantry could be a good alternative to peltasts, although they are not as common.
I know you don't care much for Elephants, but for some extra punch they can be quite useful and Carthage should easily be able to support them once the economy gets going.