Another option, perhaps more drastic, is to move past legacy forms and controls and use Content Controls. Create a Form Using Word Content Controls Don't use protection for filling in forms but one of the editing restrictions applicable to Content Controls.

If there is a valid reason to use legacy form fields, fine. Otherwise, this method cripples many Word functions.

Greg Maxey's Content Control Tools contains a utility to convert legacy controls to content controls. If you use this, do it on a copy of your document in case you do not care for the result.