If it makes any difference, I shot a longbow with 3 under the other day...and seemed to shoot it well.
Think you just answered your own question. There's no reason a longbow can't be shot 3-under. Just ask Rod Jenkins--he won the IBO World Championship in....'04, I think. He won the recurve class, shooting a longbow 3-under. He's gunning for another WC this year.
Chad