I'll chime in here, since I work in corporate proposals with what seems like a similar heading ("section") structure.

In my experience, creating the new paragraph as a new heading and then restyling it to, for instance, body text, will indeed revert the headings and cause no link problems; word manages the links well. However, I can understand your concern with a large doc.

Therefore, how about this: with hidden characters showing (the paragraph sign (pilcrow) button selected from the Paragraph group on the Home tab, or simply press Ctrl+Shift+Alt+S, which toggles this view on and off with repeated applications), simply select a paragraph mark at the end of a body text or other non-heading paragraph, copy it, and paste it at the front of the heading where you were pressing enter previously to get the new paragraph. You will get an empty text paragraph, as long as you have selected Paste options in the Word options/Advanced to have "Keep source formatting" for pasting from within the document.

Best,
Ulodesk