These guys set out to sail from Sweden to New Zeeland in an Albin Vega. They changed their mind and the boat is now for sail (edit - yes it is indeed for sail but also for sale...) in the Caribbean – probably well equipped. The Vega generally get’s good reviews and fits your price range with plenty to spare. I grew up in one of these and may be positively biased but anyhow... The boat can certainly take a lot of beating. The website is in Swedish but there is a cell number at the bottom of the page.
Have fun, I kind of envy you. Sounds like the perfect thing to do in times like these.