Might not be possible due to hardcoding, but instead of peeking, how about reducing strafing movement speed?
That would force people to move forward most of the time, only using strafing for slight adjustments.
Much like peeking, only without having to code a new animation.
Would make close-combat less silly too, people would actually charge each other instead of running and jumping in circles around each other at point blank range hoping they'll hit first.