The Alligator bridge has a closed height of 14', maybe more if you take the span to the west of the lift bridge. That will accommodate most trawlers if you lower your mast and bimini. But there is another route that has a bridge height of 45 or 65' depending on how you get around Roanoke Island.
Starting from the Oriental area if you head NE up the Pamlico Sound, past Ocracoke and towards Manteo you can go to the west of Roanoke Island if you can clear the 45' northern bridge. If you are in a sailboat you can go east of Roanoke Island, past Manteo and then back west once you clear Roanoke Island to get around that bridge. The water is a little thin on this second route and the channel is a little narrow, but if you watch yourself you will make it and carry 6+' the whole way.
Either way, you only add maybe 10 miles versus the Alligator bridge.
Then you join up with the Coinjock route in the Albermarle Sound or head further west towards Elizabeth City for the Dismal Swamp route.
David