You don't really want a Point To Polygon distance, but a Point To Point distance, with the second point being the polygon vertex furthest removed from the outlet point.
make a loop to cycle through your outlet points. For each:
create layers of (1) just one outlet and (2) just the corresponding catchment polygons.
use the verticies to point tool (needs ArcInfo, I am afraid) to convert the polygon(s) to vertex points
use the near table tool to get the distance (and direction, if you want that too) of all these points from the outlet
select the point in the near table furthest from the outlet to get the greatest distance (and direction) from that outlet.
blow away the layers and point table; then do the next outlet point.