I'm surprised nobody has mentioned that your cost estimates seem too low. I'm not in a position to correct you as I've never done what you plan to do. However, I have looked at boat prices and I have never seen a boat that meets your purpose and that you could buy in sail away condition ("drive off the lot") for $5,000. For a 28-30' boat, I imagine you are over your total budget just to get the boat in a seaworthy (and 2-year-live-aboard worthy) condition.
Here is a blog where a person has just completed a similar goal ( The Bahamas - Costs
) and posted the costs. I encourage you to read the whole blog... and for what it's worth, I saw that boat is presently for sale. Also, keep in mind this is a small 26' which is much less in size & cost than a 30'.
I encourage you to set and reach your goals so this is not meant to discourage you but to make sure you aren't foiled by incorrect estimates.