I am from California, but I've put a lot of stamps in my passport over the years and I've talked to a lot of people, so I'll try to help you here.
1) The Caribbean: You live there, your job is there, but -- what are the available resources for transitioning? Do you have nearby access to a gender therapist and an endocrinologist? If not, is there a knowledgeable, LGBT friendly doctor who can prescribe hormones and is willing to do so on a letter from an online therapist? Are you going to be able to get hormones from a reliable source on whatever island you live on? All very important questions to know the answers to before you start, and only you can find the answers by working your in person resources locally. For facial feminization surgery and gender reassignment surgery, where are you going to go? You could go to Buenos Aires for FFS or back to Europe, or to the Eastern U.S.
2) Amsterdam: Big, big advantage for transitioning. You have government funded health care, you have the necessary expertise right there, and best of all, you have facial surgeon Dr. Van De Ven nearby in case you need facial feminization surgery. Disadvantages? Long wait for government medical care, and employment situation difficult.
3) London: What are your job prospects there? London, like all of the world's great cities, can be very expensive to live in, and do you know what the English residency requirements are before you can qualify for government health care? You will either have to do private pay health care (expensive) or get on a waiting list for the NHS, and my understanding is that waiting lists for transgender care in England are very long indeed. Here is a list of services in England:
http://www.nhs.uk/Livewell/Transhealth/Pages/local-gender-identity-clinics.aspxI think your best bet is to stay where you are if you have good employment, and try to figure out your resources. If you have enough cash you could always fly to Miami for your medical care but that is going to get very expensive very fast.
Good luck with whatever you decide.