I would Google "CCI Primer Misfires" and look thru what you get. It seems to be a somewhat known issue that CCI primers are made from a harder alloy than other primers and can cause issues in some guns. Seems USPSA pistol shooters are well aware of this.
Check this link: CCI or Federal Primers?
Your issue may well be a light firing pin and weak spring. But why does that same same pin and spring work with other primers? Seems to be a fact that CCI primers can have issues in some rifles.
Sounds like you have found the utopian load for the gun and changing spring/pin may well be what will make the gun shoot it consistently. But in the end, it is the CCI primers that are out of spec, not your spring or pin...
Some folks have shot CCI primers for thousands of years and never had an issue. Some cannot get them to work in a particular gun at all.