I've been contacted by someone who has a lapband and is a grazer. With their permission I now post what they said:
Im a grazer and Im doing great on the band, been less then 7 weeks and Im down 35lbs and my grazing days are a thing of the past, the only reason I bring this up is I dont want other grazers to read your blog and lose hope.
So it seems the lap band can help a grazer. I got my info from the dietitian, but it always pays to ask someone in the know. Thanks for the comment.