If you have full confidence in your recently purchased Grand Banks, then you can cut from Anclote Key (outside Tarpon Springs) straight over to Apalachicola, weather permitting. At Apalachicola you can get into the ICW and head West. Steve can tell you more about that than I can, since it is his stomping ground. :-)
If you do not have full confidence, then head up north from Anclote Key to Steinhatchee (I stopped overnight in the Florida Barge Canal when I did it last time, but a faster boat can make it to Steinhatchee in one day). The Sea Hag marina at Steinhatchee can handle your boat on an outside 'T' slip, but it is the only marina there which can do it, so you will want to check with them ahead of time.
From Steinhatchee you can make it to Carrabelle in one day, with a transit slip at The Moorings marina, then on over to Apalachicola the next day. Or, if you prefer to anchor out, just go inside behind Dog Island at the West end, and anchor in the cove there. Plenty of water and good holding.
Kind of a deserted run, now, and not good cell phone covereage. Also lots of skinny water if you head north from Anclote Key, so have charts. :-)