Actually on the BP ( guess you mean the BP) the delts & triceps get most of the pushing act. The BP it's self is not a prime exercise for the chest/pec's. There can be less stress on the joints if the bar is allowed to touch or slightly bounce off the chest during the lift. Stopping with-in the 90 degree range may not always be the best idea. If DB's (or a crampted pressing bar) are used, than a fuller stretch is acheived on the pec's and results in more pec recuitement/development. Though a fuller or over extended stretch, with max weights, could cause more joint/musclar tear damage when doing DB's rather than a BB.
If that little hair of your's, beyond 90 degrees, causes pain than there might be a potentional injury in the making. Possible that the shoulder girdle is not flexable/warm-up enought before serious BP'ing also. Might explore different grip/hand positions.This would include the position of the elbows during the lift. Might also set the bar on the heel of the palm when BP'ing rather than a usuall gripping action. A false grip (thumbless) would be used in this regard. Good Luck.
SideBar: You seem to be throwing around a lot of impressive weight suggested from some of your past workout post. Mind listing some of the poundage use in one of your typical workouts?