Thanks first for a coherent and well thought out question. I'll just list a few thoughts that come to mind from my experience going from a T2i to a 5D3.
1. The 7D is a great camera and does many things well. However, if you get that, you're buying yesterday. It's now approaching its fifth year -- and in many ways it's about to be eclipsed by the new 70D. Personally, I believe it is soon to be replaced with a stunning 7D2, however I also think Canon could simply abandon it as the market may be compressing.
2. The 6D doesn't seem to have the sophisticated AF capabilities (and FPS rate) of the 7D, but you seem to suggest that isn't a priority for you.
3. The 6D has WIFI capability, and that may open up interesting new avenues for you. It's a lot more than social networking as it provides access to a lot of fascinating technological capabilities -- and I think that will expand. Eventually there may be things available to WIFI cameras that really excite you. And you mentioned the possibility of learning new things -- well, here's one. That may also play into the change in memory card type (and expense) for you -- if you can offload the memory using WIFI, you may need to buy less overall card storage.
4. With a 6D you'll see a huge change in your focal length capabilities. On the good side, in my opinion as I love wider angles, you'll go down to a true ultra-wide with the 16mm end of your lens. Again, you'll learn something new as you adapt to the issues of getting good wide angle pictures. On the other end, you'll reduce your reach from 320 to 200. For your sports shooting, that may seem crippling. You can get it back with an extender, but that's more expense. You may want to really ponder all this as your current walkaround lens (the 16-35) is a 25-56 on your current camera. You may feel really constrained by only going to 35mm on the long end of your walkaround.
5. As others have said the image quality of the 6D will give you a quantum leap in improvement over what's currently available in crop sensors. It will provide new challenges, but again, you said you wanted to learn new things.
6. While I would not recommend selling your flash, you will find the high-ISO capabilities of the 6D will change the way you look at light -- and your images may take on a new look.
Lastly, you may want to keep your eye on the new 70D. It may provide a good alternative, but it may also not be available for your Florida trip.
Good luck with whatever you decide.