InDesign wrapping table data cell content in Paragraph tag

As we continue to tune our remediation process, we're finding one aspect to be a real waste of time.

In order to provide a cleanly accessible PDF, we're being told to strip paragraph tags wrapped around content inside TDs.

However, the only way we can see to style the text content within the cells is to use paragraph or character styles - which automatically adds a P tag to the content on export to tagged PDF.

Is there any way to remove this tagging? It's a lot of work to strip…every…cell…of…a…P…tag.