I’ve read a lot of topics on the Hunter 340 not being the “blue Water” cruiser. This part I get and I agree on all accounts. She’s not ! I would not personally select or choose to cross an ocean in her. I was on a Hunter 36 and was caught in some weather 25-30 knots winds unexpectedly. It handled it well as expected of any boat in my opinion. I would like to cross Florida to the Bahamas and possibly a Cuban crossing. Is the 340 capable of handling the unexpected like the 360. I never go out in a window of heavy seas or forecast bad weather but occasionally the unexpected occurs. 25-30 knots as an experienced sailor will the 340 handle as well as the 360 ?
From my experience there is a huge difference between wind speed off shore and seaway conditions. The wind inshore tends to be episodic -- what you have is generally driving the seaway. That of course isn't in areas with current conditions that accentuate wave frequency and combinations of directions. Offshore is a different condition -- the same wind speed conditions can produce very different wave patterns. Mixtures of the swell and wind wave patterns, when combined create a very different 25-30 knot experience.
It's in those circumstances I believe that a boat like the Hunter 34 and 36 get tested a bunch. I would think that MOST OF THE TIME, if you pick a decent weather and sea state window, you can get to and from Cuba and the Bahamas without much incident. In both of those situations you're crossing with currents that sometimes get countervailing currents, swell patterns, and winds. The Gulf Stream, for example between Florida and the Bahamas in any significant wind that has a northerly component is going to beat you up. What boat likes being "dropped" off of square 10' waves? As importantly, what crew will enjoy or tolerate that for long?
If the Hunter 34 (or 36) is in good shape, you enjoy sailing it as you do, then I'd not let the notion of a little trip across 100 miles (or so) of ocean change your view of the boat. I'd just make sure, your boat and you are ready and remember: One of the most dangerous objects on a sailboat is a calendar.