What do you mean by that - will you stay put in one place? Or are you going to move around in that area? If you are planning to stay in one place, you could simply buy something like a Brazilian hammock locally. I don't know if hammocks are a part of Jamaican culture, though.
Don't we all. Unfortunately a hammock that is comfortable for one person can be uncomfortable for another one. I hope you have some time left before you go, because the only way to find the most comfortable hammock is to try different hammocks. If you can,
visit a hang in your area to see different set-ups and maybe even test one or two hammocks.
That depends on your metabolism. I would certainly need insulation. But I would even at temps of 100°F... Still, an underquilt is a good idea, especially if money is no object.
If there are mosquitos, then yes, get a bug net.
Again, that depends on you. I never travel anywhere (not even when staying in hotels) without my down sleeping bag. I've been cold too many times, and I hate being cold. I would think it's a good idea to take at least a blanket and a better idea to get a top quilt or sleeping bag. Especially if you don't have to carry your gear it's better to have and not need it than the other way round.
A top cover is no replacement for a blanket or top quilt. A top cover will only keep the warm air in your hammock. It's like a double walled tent. Would you sleep in a tent without additional insulation? If not, get some insulation to use on top.
Unless you go with a very lightweight fabric (like 1.0 or 1.1oz), durability should not be much different. If you are rough on your gear, get a very heavy fabric.
Most people only get a double layer hammock because they want to use a pad or need the additional weight capacity (which you don't). But more and/or heavier fabric also changes the lay of the hammock. Many people like to shave weight with a 1.6oz single layer hammock, but for me, any nylon ripstop under 1.9oz is too stretchy to be comfortable. So I only use double layer hammocks. But I also like that I can add more insulation when needed. I often put a piece of Reflectix between the layers to boost the warmth of my underquilt.
If weight is not important and you don't want/need a stretchy hammock, I would say get a double layer hammock. It gives you options. But again it would be wise to test different hammocks before you leave.
A tarp protects you from wind and rain. It doesn't insulate. A hammock (without top cover / sock) plus tarp is comparable to a single walled tent. A hammock with top cover or sock plus tarp is comparable to a double walled tent. Unless you sleep very warm, you'll need a blanket, a top quilt, a sleeping bag or similar insulation on top.
As mentioned, you can get synthetic insulation. Apparently, synthetic copes a bit better with high humidity, although I think that water-resistant down is not really performing any worse. Both will lose warmth when humid. Down is lighter and packs a lot smaller. It's also more durable - synthetic will lose more loft over time. The difference will be greater the more warmth you need. Synthetic can outperform down when used in summer quilts - but the more warmth you need, the better down will be.
At around 6' you're on the border. You might be just as comfortable in a 10' hammock as in a 11' hammock. A 12' hammock is overkill, in my opinion. I'm 5'4" and I own hammocks from 8' to 14'. My most comfortable camping hammock is slightly under 10', my most comfortable indoor hammock is 11'. I don't really gain more comfort when using even longer hammocks. And from my experience, fabric and hammock design are more important than hammock length. I will never be comfortable in a 1.1oz nylon ripstop hammock, even if it's 15' long. But my 2.6oz 10' hammock is as comfortable as my 2.6oz 11' hammock.
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