There has to be a reason why your climbers are doing this, not enough sunlight lower down possibly? Which clematis do you have as it makes a difference to the time it can be pruned but if there is an underlying problem it will still grow bach to the top of the trellis. In fact C. montana will do so regardless.

If you cut them all down to about a foot, all will produce new shoots at ground level - but you likely won't get any flowers. Jasmine reaches 35 feet high by 12 feet wide; honeysuckle varieties vary between 10-15 feet high depending which one, and clematis, depends on the variety - if its a hybrid with large flowers, between 9-15 feet, if its a species like montana, up to 35 feet. Prune group 3 hybrid clematis are pruned by mid February down to about 8 inches, otherwise the first 6 feet of growth is just bare stems with the new growth at the top, but most of the others don't need much pruning other than a bit of a tidy up.

Unless your trellis is 15 feet tall and about 15-20 feet wide as a minimum, there's insufficient room for all these climbers, so you might want to consider removing or relocating a couple. Jasmine takes up so much space its best grown on its own.