"Best case is I get an extra day.  I presume there are sites on Nym outside the park boundry"

there is a campsite close to the Nym to Batch portage - on the point or near the point that is on your left as you make the final approach to the portage.  That is outside the park - no idea if it is Crown Land, or private, but I'd guess Crown Land, as there aren't any cottages on that shoreline in that vicinity.