Tiare,
I think I can be of some assistance regarding Uitvlugt and Port Mourant.
At one time every sugar factory in Guyana had its own distillery, and there were lots of these. The Uitvlugt distillery was in Uitvlugt, West Coast Demerara (about 10 miles or 16 kilometres west of Georgetown), while the Port Mourant distillery was in Port Mourant, Corentyne, Berbice (about 90 miles or 144 kilometres south-east of Georgetown). So strictly speaking the Port Mourant rum isn't a Demerara rum but a Berbice rum, Berbice being the county to the east of Demerara.
It isn't quite as complicated as I'm making it sound

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Basically, these names are simply the geographical locations of where the distilleries used to be. Apart from Uitvlugt and Port Mourant, you might be able to find Enmore, Albion, Blairmont, Skeldon and if you're very lucky Rose Hall.
Now, there's just one distillery left - Diamond, East Bank Demerara - and all Demerara rum is distilled here. Even XM is distilled at Diamond, and then aged and bottled by Banks/DIH at Thirst Park, just outside Georgetown.
I was in Guyana in March and would have liked to visit the Diamond distillery, but it was closed for maintenance

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