One of my headings is mysteriously coming up as a link in my CPT Archive

Your query here is fine. It’s the only way to split it up into sections like that, but it belongs on a page template, not the archive. Archives should always use the main loop for its contents. Make the post type private to turn off the archive and just use your queries in a page template.

But for the tag issue, queries are never going to insert markup like that. Queries don’t output any markup at all outside what’s in the content. Your problem is that the content in the previous question, “What insurances are currently accepted by Summit?” isn’t closing a link tag properly:

or please <a href="https://summithmeinc.com/services/insurance-billing/">refer to our page on insurance billing for a list of current insurance companies we work with<a/>.

That <a/> at the end needs to be </a>.

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