I really don't think a longbow or a curve groups one better than the other.
I think this is correct. On another site there is a member who did piles of chronograph testing using a mechanical rig for consistency in the draw and release. He said he quickly learned to only shoot one arrow at a time and retrieve it from the target or the next would just Robin Hood the first one every time. This was for a pile of different bow designs and he never found one style to be more accurate than the others.
I think it is my release that I have to work on...
If you want accuracy I would suggest looking at what the Olympic recurve shooters do. They are the kings of consistency with a finger release. Of course, shooting 100,000 arrows a year with high quality coaching will improve anyone's performance...
What are your guys feelings on a window that is cut past center for accuracy???
The less the arrow has to paradox the more consistent it is going to be along with being less sensitive to arrow spine. I suspect closer to center shot is also more forgiving of a bad release but I don't know that for sure.
Mark