Sounds like you have the evidence I spoke of. Good to know!
I wouldn't bother to climb with a well found aircraft, it's not worth going over 7000'. From 7000' the likely hood is you will find a boat or ship to ditch near that will be able to pick you up. From 7000' you can also clear the Gulf Stream, but I still wouldn't do it single engine if the northerly wind component is above 12 knots. If it is, it
will be rough in the Gulf Stream, rough enough to get you killed on the pick up. The bigger the ship, the better chance they have a fast rescue boat with a trained crew, so if you can fly base/final just over the height of their wheelhouse 100' offset to the side that you need to turn to. If you have altitude to spare, cross his line of travel or even spiral down in front of them. If you have the choice of a ship or a green landing craft, take the ship lol, it's a long rough ride on G&G's landing craft.
What you have going for you in the Bahamas is warm water. You need a smoke and pyro flare for "the last mile" of a pick up in rough weather. If you have the choice, you want to do it on a still air day, or a southerly breeze, or even direct east, just not strong ene,ne, or even moderate ne or n. When the wind sets counter to the current, it beats us up on big boats. A pick up out of the water is life threatening, you better be ready. That's why ships are best, they'll launch a RIB and have guys to snatch you. We had a helo pilot pop the floats right out infront of us one time. I had a 200 tom crane. We just pulled up alongside swung a sling over to them, the pilot wrapped it on the hub and we just lifted them on deck. 5 people rode an autorotation into the GOM and didn't get wet. The water was like a millpond out there that day though. When the seas are over 6' it becomes hard to see you, that's where smoke and flares come in. If you're going to have a 12ga flare pistol, buy at least one SOLAS grade parachute flare. They come in a tube. The people that rent you the raft probably can also rent you an Olin flare kit, which since you will have to fly in the day, will be good enough. A dye pot is nice as well because it also usually has shark repellant. Now I have heard, heard mind you, that having 9v batteries in your pockets repels sharks.... Now I see where the claim may have some validity because the sharks have a galvanic sensitive organ similar to nerve that runs around their equator. I could see where 9 volt batters in salt water could set up a current field that a shark may not like. OTOH, it may set up a current field that makes it horny...
I have no clue...
Best thing is to have a vest that also contains a manual trigger CO2 built into it. Flares and floatation should be on you, but even in winter, the water is warm enough...
Oh, if you ditch next to a cruse ship, you'll probably get a cruise out of it...