You asked - Would these be effective to achieve my aim?
First I would identify what is the aim of your department? How do you support the QMS? You mentioned audits. I agree with the statement KPI's for KPI's sake likely wont be effective.
But, if it is of interest, I have used the following metrics to determine how audits are going:
1. Are audits being performed per the schedule, during the time period they are scheduled for and per what they were supposed to cover (percent). I should note that sometimes you need to do an "emergency" audit because something came up, but that shouldn't be the rule.
2. Have a person independent of who did the audit "score" the audit. This would imply having some grading criteria.
3. Were findings from the audits turned into corrective actions?
4. You did mention corrective action cycle time, but not all corrective actions are created equal. We preferred to use percent corrected by due date, and also, how many times did the due date get extended.
5. We also did effectiveness reviews of corrective actions and graded them.