Damned if you do, damned if you don't. But enjoy Jamaica. There's nothing wrong with wearing a hat and sunbathing around noon when the sun won't hit your lips.
I would agree about shea butter being the best natural option for a maybe 30 minute contact with the sun. I always wanted to research this topic more, but instead moved to Portland where the sun isn't really a problem. Now I'm in Northeast Brasil during the rainy season so basically I'm doing long-term supplementing with Vitamin D capsules.
I'd be really interested in a survey of how much sun peeling lips sufferers get on average. Due to fears of developing actinic cheilitis (a much worse condition in every sense) I wouldn't be surprised if we all get little to no sun on average.