You could call United and change the fare the fare to a W (lowest class useable by an SWU I believe).

So if you know that there are NC seats available, then you can up the fare from S-->W and then apply the SWU.

If there aren't any NC seats available, then you can decide if you want to pay the extra money to up the fare basis (probably not that much) with the risk that your waitlisted upgrade won't clear.

EDIT---I discovered from later posts that there is now a change fee for upping the fare basis, so I removed the line that incorrectly stated there wasn't.