It's a puzzle but it probably needs encouragement (right from the start of growth in spring) to "force" it towards the trellis. Maybe something like dental floss would help guide it.
I do realize you said you used wires, and I'd have thought that would have worked, but it obviously didn't. Even your photo shows it tried to climb, probably last year. I don't know why it didn't continue upwards.
My only other thought would be to replace the clematis with another one (different cultivar) that would happily climb. Candida Lanuginosa is also white and climbs 20' here.
