As usual, Stephen's comments are worth considering. But to start, let's go back to the beginning.
Upon completion of the purchase in Miami, how are you planning to register the boat? If the answer is 'I wanted to wait...' then the reality is that you'll be cruising a stateless vessel. On clearing into the Bahamas, Bermuda etc. you'll be asked to present the ship's papers and, if stateless, you'll only have your Bill of Sale. Depending on the official and the nature of the island culture, that may be enough to invite the local Customs Office to consider whether you are liable for their form of tax; they are not required to honor any reciprocal agreement re: foreign flagged vessels in their waters simply because you are not 'flagged'. Cruising without ship's papers (registration or documentation) IMO means you assume maximum risk re: taxation.
Florida offers a 90 day permit (see the Dade County Tax Collector) for vessels purchased but not intended to remain in Florida. That will give you "something" re: registration but I don't think it will be very impressive to a foreign customs officer and in any event you may need that time period to prepare the boat before departure.
My suggestion - to remedy this first problem - is to consider the cost of registering the vessel in one of the non-sales tax U.S. states; you can find a list of these at www.boatus.com/gov/state_boat.htm
E.g. both NC and SC are not too far away, neither levies sales tax of substantial amount, and personal property tax is probably voided if you have the boat out of that state on the day of taxation.
Assuming you arrive in the Azores with U.S. state registration, I suspect you will be able to avoid taxation on entry into the EU...but remember that you are liable for VAT and they could decide they are going to enforce that rule. I believe Portugal is currently close to the UK's 17.5% VAT rate, so for you perhaps this would acceptable. In case you haven't been there, all the clearance ports in the Azores are well staffed and equipped, the officers come from the main Portugese mainland ports for rotation duty, and things are done properly (if also very graciously). This not a backwater destination.
An alternative is to register your boat (e.g. SSR) in the UK. Start by reading Notice 8 published by HM Customs on their website; very helpful and representative of what is enforced in the UK. This would be my choice in your shoes IF I had the RCD issue sorted (see below); remember that this does obligate you to pay VAT on arrival but you seem prepared to do that. Alternatively on arrival, you can place the boat in e.g. St. Peter Port or Guernsey and you'll be VAT exempt...but have to travel each time you use the boat. And BTW I found the sailors least savvy about VAT as it relates to boats coming in from outside the EU are EU sailors, which includes Brits. Rather than go to one of the YBW BB's, I'd go to the 'source' which is HM Customs. They are, as you no doubt know, both polite and helpful - even if every office seems to have their own view on these matters, which is why I recommend starting with Notice 8.
Have you resolved how you will deal with the RCD? This EU mandate - http://europa.eu.int/comm/enterprise/newap...t/reccraft.html
- means, for you, that on arrival in the UK and if UK registered, your vessel is immediately eligible to be impounded at the dock because she is not compliant with the RCD but registered inside the EU. Some HM Customs folks are very rigid about this; others less concerned. One of your countryman, on sailing his SSR UK-registered boat to the W coast of England from Vancouver, Canada was immediately told the boat was not seaworthy, he was subject to be big fine, and the boat was locked to the dock. It's been a fairly notorious incident and Ian wrote a great article on it in one of the YBW magazines (YM, I believe). You want to have RCD sorted BEFORE you arrive in the UK *unless* you arrive as a (state) U.S. registered vessel.
You've got several related but distinct issues here - VAT, ship's registration and the RCD - and they each can be complicated. This is one of those nuisance issues that takes time but, if not done thoughtfully, can create lots of bureaucratic hassles later. As for sailing off to Malta to register, that would be your cheapest option IF the VAT rate there remains really low - I hear various percentages quoted and don't know how current any of them are. BUT that takes you on a different cardinal heading and I gather that's not in the cards. Of course, you can always stop in Gib and register her absent VAT; I don't think that's any different than registering her in the Channel Is.
Good luck to you; if you'd like a bit more info on VAT as it relates to boats & sailors (as seen from a non-EU perspective), I've written a piece on that topic which is found at www.svsarah.com;
select 'WHOOSH' and then choose the individual article.