Can you detail how you're trying to accomplish this? It's an interesting concept, and I'm all for people trying something different. What are the dimensions of your arch? How have you situated your Limelights in regards to the arch? I would think to really push the vertical growth, you'd need to prune for basically one strong lead, and be brutal in keeping everything else from developing too much. Depending on how wide your arch is, you might consider doing four of them, one on each corner, and then training them almost like an espalier, keeping the strong leads, and training the side shoots to meet each other in the middle, but that all depends on what kind of arch you have. What a neat idea.

Generally, think seven to ten years for a mature paniculata, but who knows what you might get with the kind of pruning this project might take. Perhaps somebody with experience creating a tree form from a Limelight might be able to speak on growth rates.