Here's an answer to my own question, with a little help from customer support. They said that it's pretty complicated inserting an html page break in the exact form itself. A work-around is to edit the exact form html in QuickBase itself. Go to the Homepage for the application itself, then Settings --> Pages. There you should see the Exact Form. Click on it and you'll be able to edit the html.
I pasted in this simple html page break where I needed them:
<p style="page-break-before: always">
And it worked. Downloading the exact form back into the word macro, and then saving it back to QuickBase resulted in loss of the page break for some reason, so I'm having to re-insert every time I do this. There's probably some better html code that won't get stripped, but this works well enough for me.