Map the 'tighten straps' function to an easily accessible key and that will bring you right up to the gunsight and dampen the TIR motion for finer control so you can line up your sights.
It will restrict how far to the sides you can look while in this mode but you only really use it when you're closing in for the shot anyway and should help out quite a bit.
When I get home from work I'll post an updated TIR profile you can use as a template to tweak to your own comfort level in this thread:
http://forum.1cpublishing.eu/showthread.php?t=20716