As far as the Keys are concerned, your only viable route is the Hawk Channel on the ocean side of the Keys, no way is the ICW route down Biscayne and Florida Bays an option with your draft...
The first place I'd recommend cutting through with your draft would be the Moser Channel at Marathon... You could probably make it thru the Yacht Channel up from Channel Five west of Islamorada, but you'd be VERY close to the bottom thru there. Since there's not that much to be gained distance-wise, I wouldn't recommend it, I'd go on to Marathon, instead...
However, as long as you're that far west, you may as well consider going out to Key West, anyway - if you're inclined to spend any time there, that is...
Main problem with the Hawk Channel and your draft, is the dearth of good, protected anchorages or marinas between Miami and Marathon... The Ocean Reef Club is your best bet, but it's a private club, and I'm not sure what their policy is towards accepting transients is at the moment. Otherwise, you'll likely wind up anchoring somewhere in an open roadstead, tucking in behind Rodriguez Key is one of the few spots you can gain any protection at all, but not if the breeze is NE-E... And, you really don't want to be running the Hawk Channel much after dark, plenty of crab pots thru there, for one thing...
As for the ICW between Norfolk and Miami, don't necessarily rule it out because of your draft... Most of it will be do-able, you can certainly go inside Hatteras to Morehead City... Between Morehead and Little River, and then Georgia and some spots in FL north the St.John's River are the most likely trouble spots (don't even THINK about doing the ICW in Georgia south of Sapelo Sound), but otherwise most of the ICW can still be an option for you... Not to suggest you'll never find the bottom somewhere, but by playing or waiting for the tide, you should always be able to make it thru...
And, for the most up-to-date info on the changing conditions along the ICW and east coast, this is probably the best resource:
Cruiser's Net