OK, with some help from my friends from Stack Exchange, this is solved.
The way to solve this is similar to the way we add pre-header text everywhere else - it just needs to be Outlook specific.
This solved it for me:
<div style="font-size: 1px; line-height: 1px; display: none !important; mso-hide: all;">Add pre-header text here. Make sure you have a lot of text since the default Outlook 365 preview is 3 lines.</div>