Where to start!? First of all greetings from your neighboring island!
I'm Jamaican but live in Florida now and have been fishing out of Hobies for 4 years now. In that time I've owned 4 Hobie Mirage models: Sport, Revolution11, Outback, Revolution13 (in that order). You will not find a more capable craft for kayak fishing, and I speak from experience nearshore (mangroves & grass flats) and offshore (up to 3 miles out and as deep as 400ft). On to your specific questions...
1. What are the benefits of a SOT vs SIK in ocean offshore fishing? I cannot think of ANY advantage offered by a Sit-In kayak where fishing is concerned. SIK are great for covering ground; they're sleek and fast and are more for touring. They are usually long and narrow and can be a bit tippy for the beginner. They are designed to be used with a rubber/neoprene skirt to keep water out of the kayak from waves and roll-overs. This can be uncomfortably hot during summer in our location.
On the other hand, Sit-on-top kayaks offer a much more comfortable design for the tropics: you can jump off, re-enter, or splash water into the cockpit, all without worry of taking on water inside the hull. Hobie's molded in rod holders and recessed tankwell mean you have space for rods, gear, and a catchbag. When properly mounted and sealed, you can have fish finder and gps installed on hobies too!
2. Mirage system have any good benefits in off-shore type fishing?YES! Three major advantages. First, your legs will not tire out as quickly as your upper body, so you can typically cover more water with a mirage drive than paddling. Second, you are pedaling so your hands are free to handle rods/tackle or you can use the mirage drive to chase down bigger fish like tarpon when you hook up and start fighting. Third, if you catch a fish you wish to revive and release (like a sailfish) you can easily do so with your hands while you pedal the kayak.
3. Why is a Hobie Angler worth the extra$ rather than a Quest?I think you need some clarification here. Did you mean the Pro Angler series of Hobies? Because yes, they are expensive! But they are expensive because of size and complexity. For a few hundred less I really recommend the Outback for you. At 205lbs, I was very comfortable in the Outback, and you probably will be too. It offers 4 molded-in rod holders, 400lbs capacity, excellent stability, and is very offshore-sea-worthy. The paddle kayaks are always going to be cheaper since they do not have rudders or mirage drives, and if that's your preference there is nothing wrong with that!
4. How much stand-up fishing have you done and if so you probably recommend a SOT with a swiveling chair, correct?I do not stand up to fish, it makes no difference offshore to me and the kayak I have chosen to use (revolution 13) is hard to stand up in anyway. However many of my friends do stand up if/when they are fishing inshore or on the flats. For that you need a kayak you are comfortable standing in and this is where a sturdy wide kayak like the Pro Angler really shines. With that said, you can still stand in an Outback, though some practice may be necessary. None of the Hobies come with a swiveling chair, and actually none of the fishing kayaks on the market do either, it would only be a detriment to stability as you are paddling/pedaling.
5. Bottom fishing and casting...I do a lot of vertical jigging in 300'+ and I feel very comfortable doing so. Resist the urge to sit "side-saddle" until you are more comfortable with your own balancing skills, and even then I don't do this for fear of sharks, or big amberjack pulling me overboard. Casting is also fine in the kayak, but as a powerboat person, you may need to get used to doing everything from a seated position.
Good luck in your search!
If your wife likes the Quest11, try the Revolution11. Same dimensions, but with the mirage drive.
You sound like you could be comfortable in an Outback or Pro Angler (comes in 12ft and 14ft).
PS: regardless of the kayak you end up choosing, remember to add a tether to your rods and paddle because accidents happen and roll-overs are just a rite of passage for the kayak angler. As you get more familiar with the sport and gauge the weather conditions better, you may not need the tethers as often.