Wouldn't it make sense for the Jamaican Tourism Board to subsidies and organize a series of concerts and\or a concert venue if it's something that difficult for a private enterprise to do? Tax money collected from tourism could be used to subsidize the concerts costs and ticket price. This would not only benefit the tourism industry but also the locals (think free ticket giveaway contests and\or discounted tickets at sponsor locations). Make sure the main act comes on at a decent time and then let the party continue in Jamaican style.
Since most tourists are only in town for a couple of weeks, at most, the series could consist of a revolving set of "resident" artists. I don't think big names are necessary but quality up and coming or emerging artists that want to get their name out there internationally would draw crowds if the production quality was consistently there.