The TI is a Trimaran boat, ( 3 hulls), near impossible to capsize, so the TI with it's outriggers is a much more stable boat on open sea, I'm just not sure if any of the PA boats have enough stability for offshore, (I strongly doubt it), the PA line of boats in my opinion are more for fresh water lake and river fishing, or protected waters like the intercoastal here in florida. I have never seen any PA out past the breakers in open ocean around here or in the keys, I see quite a few PA's around here but all seem to stay in protected waters.
Many of us offshore guys add outboards to our TI's for an added level of safety, this doesn't mean you have to use it all the time, (with my twin Honda 2.3hp engines tilted up, the boat sails exactly the same as if the engines were not on the boat), but they are always ready to get me out of tight situations, (ie... wind changes or just flat dying completely, sudden storms, mast or rudder breakage, etc). Plus the rudder on these boats is not real strong, you need a backup steering method if your rudder ever does break while out at sea, (at least in my case I cannot steer the boat with a paddle, the boat is too big), and I'm not about to try and replace my rudder pin in 15mph plus winds and 3-4ft seas.
Lots of others using their TI 'adventure boats' to do exactly what you are planning. I have never seen or heard of any PA attempting what you appear to be planning.
Every year in March there is a 300 mile race called the everglades challenge from Fort Desoto fl to Key largo fl, (
http://www.watertribe.com) Typically most years there are over a dozen or more of these Hobie adventure boats, (both AI's and TI's) entered in the race, all must carry tents, food and all supples on board including water ( 3-4 days worth because there is no fresh water at all in the everglades ( just fyi).
Basically these guys are currently doing pretty much what you are describing. I have never heard of anyone entering the race with a PA.
Hope this helps you decide
FE
Edit: of course you don't need twin outboards, one will suffice just fine, our TI is specially custom outfitted for offshore with massive sailsets and outboards ( because that's what we use the boat for, (diving in the keys)), plus we sometimes travel great distances with ours, our current daily max range is around 100 miles.