I know it sounds crazy but try these settings for a bit and see if you still have any issues. I know, tech wizards out there, it doesn't make sense to use these settings, I know, but it has helped me before (I think, unless it was placebo). It can't hurt to try it.
cl_cmdrate 100
cl_interp 0
cl_interp_ratio 1
cl_lagcompensation 1
cl_pred_optimize 2
cl_smooth 0
cl_smoothtime 0.01
cl_updaterate 100
rate 100000