First of all I am glad that your game worked out in the end. There are two different points to this that are worth discussing though.
One, I don't think you are railroaded into losing that territory. The stability system is not a system of railroading but a system of pressures, and especially on the expansion side the pressures are based on historical territory. The pressure exerted on you by holding the peninsula is not equivalent to a script that forces your collapse (or a secession) - it is always possible to remain stable enough to prevent these outcomes. With overexpansion, you can address it both by managing your population and expansion into other areas, and by generating enough positive stability elsewhere to offset the expansion penalty.
That sometimes requires making choices that are otherwise not optimal (in terms of civics or city development etc). Carthage controlling Italy is not historical, so you are pushing against history here, and the stability system is history pushing back. You have to bend a little if you don't want to break.
Second, I would like to encourage you not to view a setback like that as losing. In the context of what you're going for, it doesn't even matter - you don't need to own that territory anymore, the goal that required it is already completed, and the remaining one doesn't depend on it. Of course it would be nice to retain that territory, and it isn't impossible, but I want to foster a "roll with the punches" attitude for this game, especially when it comes to UHVs. You always have to grow and you can never lose anything is a mindset encouraged by base Civ4, but it doesn't have a lot in common with history. So for a historical game, it should be abandoned to some degree. UHVs exist exactly to give you a way out of this mindset: you don't have to ride the growth curve until you dominate everyone at the end of the game, you just have to use your situation correctly to meet your very specific goals.
As for your specific suggestions, is there really any justification for making Italy historical territory for Phoenicia? Is there really any historical justification for giving them a unique power uniquely suited to guaranteeing stability?
I am actually deliberately trying to not frame this response as "git gud", but more as encouraging the idea of "losing (a few things) is fun".