From my years of experience handling such monsters, I say without reservation that you'll lose far more time in exasperation than you will spend transferring to a clean template doc.

If you have a clean template, with only the styles you need, create a fresh doc from that. Otherwise, create the template you want, name it appropriately, store it where you wish (desktop, Templates folder, or personal folder) and create a fresh, blank doc from it. This gives you a "back-up" in case something goes wrong later, as you can re-import the styles from the template if they get messed up.

With the clean shell and monster doc side by side on your desktop, copy and paste special/unformatted text from the old to the new, or, as others suggested, copy the old into plain text, then copy and paste that into the new doc, and apply your styles as appropriate, referring to the old doc as you go for numbering, etc. If you don't want the two side by side, print out the old and set it up in a copy stand next to your monitor.

If you're fortunate, Word's auto-numbering gremlins will not make your life impossible. Happy formatting!