Could you just tie it in and train it to the support? If it's bushing out it sounds as if it's sagging off the trellis.

They can be pretty much pruned at will :-) All it will do is affect flowering to some degree but that doesn't appear to be a big concern.

My 'Huldine' is at least 15' tall all the way to the top of a small ornamental plum tree....

That's good to hear gardengal. Here are a couple of pics to see what I am talking about.

The area that I plan to trim is the lght green new growth at the bottom. It is over-running the Weigela Minuet that you can just see underneath.

The Ville De Lyon and Ramona are pretty well behaved:

As floral commented, it is sagging some as it starts up the trellis. You can certainly cut it back this year, and next year I would consider adding some wire fencing (painted to match the trellis) or knotted fishing line to the bottom few feet of the trellis. Because the wooden bars are relatively large and the trellis relatively narrow, the clematis is struggling a bit to grip it initially and is bushing out some before starting up. Clematis find it easier to grasp something pencil width or narrower since they climb by wrapping their leaf stems around their supports. So if you provide something of narrower diameter to grab near the base of the trellis, it will start climbing more easily and be less likely to smother the weigela. Or you can shift the weigela farther away from the trellis.

They all look quite healthy!