My strategy that I'm experimenting with now is to merge my damaged units as I go, and gradually replace them with foreign troops as needed. This is expensive, but it seems to be working better than anything else to keep me fighting fit.

That´s why DEI is realim. I mean, it´s logical that when you conquer a foreign land, you will only have the ability to replenish with native troops, because changing culture is something that costs time.
So I think you are doing well in the way you replenish, do it like Alexander the Great ;)

Have multiple armies in Sicily, I suggest to hold Syracuse with two (or three if you can spare it) full stack armies, leave the other two regions undefended. When Carthage takes one of the settlements (which they will, they will just send army after army) you will retake it. You can loot it each time for nice profit. Then dont waste money to repair any buildings. Rinse and repeat. Note that you dont have to worry about Carthage sending Hannibal through the Alps to attack you from the north, and they wont send a fleet directly at Rome either. Carthage will stay invested in Silicy so you can just focus all your power there.

Also your generals are going to get LOADS of XP from winning those battles, and you'll get tons of slaves too. And if you make sure to make the generals characters from other parties you'll get loads of loyalty too, both from winning battles and promoting their characters.

Oh and subjugating or conquering Epierus last settlement might also be a good idea since they will continue to be a major threat if you do not fully stop them, and freeing up that eastern front will be extremely helpful for focusing your efforts in Sicily.

Final thought, maybe make great efforts to keep peace with the closest of the northern factions, Venice at least for example. You may want to keep an army there to deter any treachery (and thus make do with two armies in Sicily).

Thanks for the tips! An update on my campaign, Carthage has fallen and I've taken the coast all the way to Egypt in the east, and the edge of the map to the west. I've hit the Marian reforms and am finishing off the last Carthaginian holdouts in Iberia.

New Question: Should I be relocating plebs and proletarii from Rome to my other provinces? I've been doing it a bit for the provinces closest to Latinum, but nothing further than Sicily. I'm curious what other people's strategies are? I'm not sure if this is intended or not, but it seems as if foreigners are able to replenish my Legionnaire units now.