Working in ArcGIS 10, I have a set of contour lines representing density of commercial square footage, and I have a set of points representing local maxima for each peak of the dataset. For each maxima I would like to find the largest contour line that contains only that maxima and no others. 

My strategy is to convert the contours to polygons, spatial join the polygons to the points, choose only the polygons that overlapped 1 point, and for each maxima choose the largest polygon, an operation that will probably happen in MS Access.

I've run into one problem - when I convert the contours to polygons using "feature to polygon", the polygons don't overlap, so my maxima only join to one polygon, breaking the method.

How can I convert polylines to overlapping polygons? If possible, I'd prefer a solution I can fold into an ArcPy script.