Now keep in mind this won't make everyone happy. There are going to be people who argue and complain no matter what. But here's at least a decent explanation for your personal sake, that allows it to fit into lore.
Everyone agrees, even lore purists, that Umbar could have easily been a naval empire at the height of it's power in the second and early third age. However as we all know it was eventually conquered by Gondor, and occupied by them. Presumably, when this happened the colonies either collapsed in in themselves, or survived independently, because Gondor wouldn't waste time claiming them.
Now normally, this would be the end of things, and Argali would be right, you would have to play as a colony like Mînbar. But it's not. The kin-strife took place, and ended with Castamir and the corsairs settling in Umbar. It's also stated that his supporters came with him, and he excepted traitors from Gondor. So we know that at this point Umbar sustained it's Numenorean population. Because the corsairs also commanded much of Gondor's sea power, and was considered a major naval threat to Gondor, we can assume they had a powerful navy, which it is reasonable to assume allowed them to retake several of the old colonies. So once again if we RPed during this era, you could Umbar you want.
However, Gondorian history is annoying, and some jackass who named himself Umbardacil decided to mess everything up. And here is where it gets more like a conspiracy theory. When Umbardaci lab added Umbar most people say it's power was crushed. He left Umabr a ruined pirate's haven in his wake, and it was only reclaimed by the Haradrim, ending the Black Numenorean line there forever. However they are forgetting several things. One, Umbar was full of people of Numenorean descent, and there is no way he killed them all, because he didn't have the time to go on a genocide! He left right afterward! Which means a good portion of them probably escaped into the surrounding area! Plus, we're forgetting about the colonies! There's a high possibility of Numenroean blood in the colonies as well, and he certainly didn't take those.
So now we've established Numenroeans reamined, let's talk about the line of Castamir. Once Umabr was retaken by the Haradrim, Haradrim royalty would take control right? Well, maybe... But there's also another possibility. When European medieval conquerors took control of new territories they often instated family members as regents over the land. Meaning that even Umbardacil destroyed Castamir's line in Umbar, there's still a good chance it survived in the colonies. But they would have to stay in the colonies and leave Umabr be right? Wrong. Castamir's line was known to be crafty. It's highly possible that they found away through political intrigue and intermarrying to regain control of Umbar, and since they already have the colonies, well you get the idea.
They still wouldn't be as powerful as they once were, but that's part of the fun, they're trying to reclaim their former greatness. I know this might not be the most logical order of events, but that wasn't my goal. My goal was to give a scenario where the Umbar you want still exists, and I believe I'v done that.