There are many threads covering "Cost of Cruising" already. And as for retiring then assuming you have some type of pension it is unlikely you will "run out of money" as cruising area and style can compensate for income.
The one thing that will cause the MATH to go wrong is TOO MUCH BOAT.
The recommended budget for a initial refit is 20% to 30% of sale price of boat given a sound boat was purchased to begin with. How much work you do yourself , What you feel you need before going etc etc.
10% of boat value per year maximum is generally considered a good figure to cover boat costs including haulouts and repairs
, upgrades etc.
A Gemini is not considered a world cruiser although I assume some with have done it.
Using a vessel at its edge as far as use will generally rack up larger repair
A new boat will have no radios
watermaters solar panels inverters
or any other toys.
Although your repair
and refit money will be pushed off some time the depreciation on a new boat is rapid and steep.
The current thinking on refit is not to install to much stuff.
Cruise for awhile before going all out on expensive complicated systems.
You may have no use for them but they will break and need maintenance non the less.
and Watermakers come to mind for some cruisers.
The Caribbean is not going to have issues of water or weather info options including local TV/radio weather and everyone at every island will have water to drink and the sea water in harbour the water may not be pure enough to use anyway.
Weight on a small cat will also be an issue for you to think about.
You did not say what area you will be cruising in but I don't think you are too far off the mark fiscally given prudent use of the kitty.