As far as I am aware what is on the island does not change. Tuna are available now, I got one on the 1st. They are not common though. Despite what the guides say all the November new fish and bugs can be caught in November. I got the last new one I needed yesterday (horsehair crab). So it can be done.
I love the smell of Coelacanths in the evening
No, you cannot get a tuna on the island due to the "season" it's stuck in. It resembles a June-July time, and is always warm and tropical. Unforutnately, you can only get tuna during the fall/winter period. I am, however in late February and am still catching tuna!
I hope this helped a tad! Good luck and happy fishing!