There is another way to influence climatic conditions with map editing only.
Of course, you will lose out on realism to some extent.
Before actually designing your island, raise the entire map a few notches.
Consider the following case study (It's not supposed to be pretty, just making a point).
I raised the entire map to produce optimal conditions for papaya - I like the graphics for these babies much better than corn. Notice to what extent the overall conditions for tabacco and coffee improve as well. And corn can still be grown effectively.
For sugar, of course, you'll still have to dig some swamps.
I'll not comment on whether or not I consider this method 'cheating' lol
Hey- after all, your island could be located inside a lake way up in the Andes.....