Cut them! With as cool as this spring has been they're probably not growing very fast right now anyway. I've seen KO's cut to the ground with a hedge trimmer that came back beautiful in a matter of weeks.

it's typically done in the spring here before the new growth starts. if you don't mind looking at a hacked off stub all winter, i guess you could do it now, but it may make it more susceptible to cold. if you do it at the right time in the spring, the new growth hides the stubble very quickly. you don't have to trim it back, but the new growth is prettier, if overall a bit less full (since you don't have old strands, too), if you do. it looks more graceful. you trim it down as far as you can comfortably do it- you'll know.

I am well aware of how aggressive this clematis is. I made the mistake of listening to a suggestion that I use it as groundcover in a certain situation. I changed my mind about five minutes later, but have been digging out (with a spade, not a trowel) the seedlings ever since. I think this obelisk will be a one-season thing. I am wary of creating too many fussy plantings that need surgical precision to control lest they become landmines. What if I wanted to go away some September? Or the unsuspecting next owner didn't know how important it was to remove every blossom before it went to seed?

It is never too late to prune a clematis :-) Yes, it could delay or alter bloom time but in a mild climate with a long growing season, it is not going to have much of an impact. When I worked for a wholesale grower of clems, the vines used to get cut back routinely every month or so just to keep the pots/vines from becoming tangled up with each other. All this did was to encourage more basal stem growth, generally considered a good thing :-) Never affected the flowering to any significance.