I grow many climbing roses, and if this were up to me, I would use the rejuvenation method to deal with this rose by doing the following next April (or whenever the forsythia blooms in your area, but not during the winter):
1) Cut the entire bush back to about 30 inches above the ground, straight across for simplicity's sake.
2) Then thin out the number of canes by first removing all hard, thick, "woody" canes that are not very viable.
3) Then remove all thin, spindly canes.
4) Leave 6 - 8 viable canes of medium thickness; they will very quickly branch out and produce new shoots next year, because the extensive root system will send all of its nutrients into these half dozen canes next spring.
5) As the canes lengthen next summer, tie them horizontally across the fence railings.
