It just seems strange to me that I can shoot the type of groups I have been shooting with that much of a left tear
You can shoot perfect scores with 6" tears - Most top archers want a tear as they like the arrow to have some character as it leaves the bow. 3" tears will not hurt your accuracy with field points.
I highly doupt your GT arrow spine will produce 3" fletched tears.
IMO, It is a matter of torgue, fletching clearance, incorrect center tune, or a combo of these.