Try a Google search, or Trip Advisor is also excellent. For example try "Marathon Key, weekly rental" and see what pops. In fact I just tried it, and it did come up with "tropical cottages" at one spot but they were booked up already.
Everything's going to be pretty pricey, too. But with 4 of you to share, maybe it will be more reasonable. You don't know anyone with a condo or time share, do you? It's great to stay somewhere that has at least a kitchenette so you can eat breakfast without having to find a restaurant every day.
If you got a spot "before the keys" that would still face you with a 3+ hour drive down to Key West. It's a two lane road all the way down the Keys with little chance of passing, and is very busy in winter. As Hetty says, Marathon is more or less halfway, so that's where I'd aim.
Or head over here to the West Coast, we have Keys too! There's a spot on Longboat Key here in Sarasota just like what you're describing, only without the kitsch. Lots of golf, and the Marie Selby Botanical Gardens, not to mention the Ringling Museum, and many other delights. You'd be able to visit Hetty in Naples on your way by.
