Brett,
it depends on what kind of trampoline you have. If it is a mesh cloth tramp, I would have bought some vinly coated cloth from sailrite and stitched it to the underside of your tramp. Overlapping the edges of the tear with 50mm should be sufficient.
http://secure.sailrite.com/itemdesc.asp?CartId=&ic=112011&eq=&Tp=You can easily stitch this material with a domestic sewing machine. While you are at it, buy needles and fitting thread from sailrite as well.
I have no experience with other trampoline materials, but I think the above should work well with vinyl and other materials also.
Qb2:
Heat guns and trampolines dont mix well! Have you tried having a friend help you so you can work on both sides?