ASL Grips come in 3 choices: Straight, Dished, Locator.
All the longbows built by Howard Hill that I've seen or held had a straight grip. A straight grip will reduce torquing the bow left or right after the shot.
A slight dished grip is comfortable.
A locator grip is comfortable and maybe perfered by recurve shooters because it's a grip style they're familiar with.
Grip dimensions. An ASL grip should be longer front to back than wide.
A good size grip is 2 1/8" Deep X 1" Wide.
Smaller hands may want 2" Deep.
Larger hands may want 2 1/4" Deep.