How manage growing stem tops of vines (Cardinal Climber?)

My Cardinal Climber is doing fine and many of the stems have easily climbed to the top of my 6' trellis. Every day I have a new crop of stems growing off the top of the trellis, waving their ends in the air like flags, looking for something to wrap around. What is the best thing to do with these? I'm torn between two different techniques:

(1) Cutting them off (off with their heads!?) on the theory that cutting the growing edges at the top will encourage leaf nodes lower on the trellis to generate new stems. If this is the best thing to do, how much of the growing stem should be cut?

(2) Waiting till the waving stem flags at the top are fairly long (9" or so?) and then manually weave those downward and sideways on the trellis so that they'll start over growing upwards but in the meantime they'll create more leaves on the way and fill out the lower parts of the trellis. What I've been doing is after I train a stem down to a lower and sideways lattice on the trellis, I loosely hold it in place with a garden tie. By the end of the day, the stem has usually gotten the message and has twined around the part of the trellis I've encouraged it to.

Which technique do you think will generate the most leaves and of course flowers?