That's a limitation of having to use Section breaks with the 'Filling in Forms' restrictions. You can, of course, minimise the gap introduced by the Section breaks, by formatting them with a 1pt font size and 0 space before/after paragraph formatting.

If you were to use content controls instead, you wouldn't need either the 'Filling in Forms' restrictions or the Section breaks. Indeed, content controls work quite happily with no restrictions at all, so you'd only need to use the 'No Changes (Read Only)' restrictions if there are portions of the document where you want to prevent editing.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]