Dear QA Patrick,
Recently I raised a major Non-conformity in a similar situation.
The new QA who was in charge for 5 months had been very busy with a lot of things.
He noticed that in the months before he was in charge, no internal audits had been done, but he himself had also not done the internal audits. He found it more important to adapt procedures. He did not make a plan, because he wanted to change all the procedures before starting auditing them. At the day of the audit no internal audits had been conducted in the last 12 months and no action plan to correct this.
I could do no other thing that raise a major.
If he had only made an action plan and conduct the most important audits as correction before the audit ......
I think the way you are handling/ planning to handle are good. Try to catch up by temporary increase the frequency of auditing. Write that corrective action plan and make sure you have management commitment.
I am sure you will be fine by this.