Starting this scenario yet again....El_Colonel's strategy is definitely the key; as long as you can stay in power and build farms, it's a walkthrough to do it within 30 years. I'm convinced that it can be done within 20 years, give or take. Socially and spiritually, this is a brutal scenario; the sooner you hit the export quota, the more suffering your people have to endure. That said, based on previous models, here's the approach that's gonna by-God do it within 20 years this weekend:
1) Give the peasants nothing for at least 10 years. With a 20+ year goal, you only have to ride out two elections, maybe three. Build no infrastructure whatsoever, only farms and (not yet sure on this) a Bauxite mine. No Tenements, no Markets, no nothing, just keep wages above the Caribbean average. The overall happiness level will still be high enough by the first election that you can win by doctoring the returns. For the second election, toss the Proles a few tenements and a pub; they'll be so miserable that they'll think you're doing them a huge favor. If you try to be nice and give them decent amenities early on, they'll just demand more expensive amenities sooner. Your Agriculture income is pretty pathetic, but by the early 60's, it's more than enough to dazzle a troop of shack-dwellers.
2) As El_Colonel states, dont bother trying to protect the victory crops, beyond adding a few extra corn or meat farms. Dont build ANY markets, 'cause it just distracts your teamsters from the prime task of hauling fruit to the docks. Likewise, shut down the cannery; it's just a chokepoint in the the fruity pipeline. Let the HoiPolloi grab snacks from the farms.
3) It appears that three Pineapple, four Banana, and five Papaya farms can do the 20-year job, if they come online fast enough and are augmented by other food sources. One of the corn farms SE of the palace is in good Pineapple country, convert it from the start and it will produce up to 36 squares of harvest in the initial bumper-crop phase. The main axis of expansion is along the south shoreline; an additional teamster office, construction office, and dock near the Archaeological site appear (??) to be sufficient. Use roads to connect every farm you build in the southern expansion to the southern dock, likewise connect all northern farms to the northern dock, but DONT build any roads that link the southern and northern hubs; the teamsters tend to go into brain-lock trying to choose a destination.
4) Be prepared to bribe, imprison, and assasinate at any moment. Investing in a prison and bank after the first election gives you a lot of options. When your economy goes bad (and it will), make sure to keep $500 on hand to snuff at least one troublemaker. Always remember: "I realized that before I could become a benevolent despot, I must first become a despot".