Tires, tires, tires.... where to start?
Assuming your Fortezza tires are 700x23's -- and if your combined team weight isn't over 330lbs -- put the Fortezza's on the tandem and take it for a test ride to see how they feel. Make sure they are pumped up to the recommended psi rating, e.g., 700x23 = 145psi, 700x25 = 135psi. If you like the way they feel ride them for a while to see how they hold up to your local road conditions. If you find you like the 700x23s but feel they are a bit harsh or you'd just like to have a little more volume in the tire buy one 700x25 and put in on the rear of the tandem to see if still gives you a comfy ride. If so, you've found your tire. NOTE: I'd recommend the Fortezza but not the Fortezza Tri-Comp.
Of course, you can do the same with the Conti GP3000s, relative to the test ride, i.e., try 'em and if you like 'em stick with 'em. 700x23 or 700x25; your choice.
You'd have to ask Dwan, Dan or Alan at Co-Motion, but my guess on the Gatorskin is the "mass market acceptability" to the average tandem buyer of the higher mileage tread life, purported flat resistance (don't know about that) and cost. At 320g, the Gatorskins are not racing tires by any stretch; you'll note that 700x25 Michelin Axial Pros come on Co-Motion's go-fast Supremo & Robusta tandems.
Bottom Line: Stick with what works and/or what you've been happy with on your single bikes to start out, perhaps going one-size larger, particularly if your team weight is 330lbs or more. Recognize that "high performance" tires will wear out rather fast on tandems, e.g., 1,500 - 2,400mi. for a new rear tire from day 1 until it's nearly worn through with a "squared-off" look to the tread. This is one of the reasons why you'll hear me suggesting that you start off with two new tires and then, once the rear tire wears through -- move the front tire to the back and put the new tire on the front. In effect, this will allow you to get 3,000 - 4,800mi out of a single tire (1/2 life on the front & 1/2 life on the rear).
If either of your current tires don't hold up well see what kind and size tires other tandem teams in your area who ride the way you ride are using. Give those a try -- perhaps even swapping out wheels for a test ride IF you have basically the same type of wheel. If they have different wheels the feedback you get from the 'tires' may have more to do with the other wheels vs your own.
My experiences? We've been riding on Vredestein Fortezza tires since 1996 -- all tolled about 25,000mi. Our first tandem was a Santana Arriva that came with 700x28 Armadillos and they came off after our first ride. I took the Vredestein Fortezza tires off one of my single bikes just so I could get ride of the "lifeless" Armadillos and low and behold, they made our tandem handle much better. I initially used 700x23 skinwalls and more recently the new all-black 700x23 & 700x25 models. In a perfect world I'd run 25's on the rear and 23's up front but that's just not a practical scenario given the way the tires wear, thus I've gotten used to the 700x25 as a front tire but I over inflate it to 145psi to regain the feel of the 23.
Other tires to consider would include Avocet's K20 models in 700x25 or 700x28: An excellent tire for all around riding.
Anyway, more than you wanted to know. Enjoy your tandem -- you picked a great model to start with and you'll find Florida has quite a few tandem teams to share your rides with.