My husband tackled this project last June and we are very happy with the results. After much research, he used seal-tite corner seal (only available on line and high shipping and handling, but great stuff) http://www.sealdesignllc.com/catalog/seal-tite-corner-seal/ and sikaflex 1a (both before and after using the seal-tite corner seal, which is like a sticky tape).
The most time consuming part was cleaning up the trim. We reused the vinyl insert because it was in good condition and we couldn't find anything as heavy duty as the original.