You could update the website to parse content controls instead of formfields, but that's another issue.

For your current setup, insert Section breaks either side of the portions you want to remain editable, then leave those Sections unprotected when applying the forms protection. When you go to apply the forms forms protection, you'll see 'Sections' in blue appear below the 'Filling in Forms' selection. Click on that and uncheck the sections to be left unprotected.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]