With all due respect, I suggest that you quit listening to the mythology and looking at out of date guides to bluewater boats. The reality is that many of the heavy displacement, full keel cruisers actually have substantially smaller angles of positive stability than modern fin keel boats, and few on the list of offshore cruisers above achieve 140 degrees of positive righting moment.
While a heavier displacement boat with narrower beam, more volume underwater, fuller keel, etc. is one valid way to go, the majority of offshore cruisers out there do not meet that description. But if that is the route that you are inclined to pursue, with your budget I suggest that you see if you can find a good clean Kelly Peterson 44 or 46.
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Curmudgeon at Large- and rhinestone in the rough, sailing my Farr 11.6 on the Chesapeake Bay and part-time purveyor of marine supplies