Did you try SuperShuttle? They used to have good prices.
I used SuperShuttle the last two times I needed to go between those airports, and they were not good experiences. You can reserve and even pre-pay a spot on a shuttle, but they don't guarantee how quickly you'll get onto a shuttle, unless things have changed in the last year or two. I arrived into Miami and went to the SS kiosk outside, and stood there in the noise and car fumes for an hour or more both times, until a shuttle that was going to Ft. Lauderdale finally showed up. And then it made many stops between the two. It took over 2 hours to get to Ft. Lauderdale, by which time I swore I'd pay the $60+ to take a taxi next time.
Of course, I figured that had to be an unusual case, so I tried it again, with pretty much the same results. I've used SuperShuttle to get from an airport to a nearby hotel, or vice versa, but I won't use them again to go from one airport to the other, or from an airport to a hotel in another city.