So did Worf's Change of Heart cost him command of the Enterprise?

Well the line is something like the "That was three hundred and nine years ago" at least in relation to when they left their homeworld. Which would place it aroud 2066 almost a full century before the Federaton was founded. Now I guess they could have wandered the galaxy for those 95 years. But there is nothing to suggest that the Ba'ku normally age any differently than humans

 

That presumes that the Federation recognizes the ring planet as the Baku's private property. The Baku are relatively few in number, and they are not indigenious to that planet. The Federation could easily not view them as the planet's "owners."

Exercising eminant domain might not have been seen as necessary.

According to ENT (augment arc) when the Baku arrived the briar patch and it's contents was Romulan territory. Later it somehow passed into the hands of the Klingons (per DS9). Later still it passed into the hands of the Federation.