Advice on Katsura (Cercidiphyllum japonica)

Katsura are appreciated for colourful foliage in the spring and again in the fall. Does anyone have experience with this species. I’ve recently taken possession of this large specimen and wonder if there is any advice available in the community.
The tree was trimmed to profile and partially defoliated early in the spring. Now I’m watching it put out some incredible growth but wondering about additional pruning once the new growth hardens off. Current growth generally has large leaves and long internodes, although smaller leaves now seem to be developing.

Trimming to profile does not seem to be the way to proceed. Shoots develop either a fan shape or bar branches at the cut end of the branch very easily. I am wondering how to encourage branch development and ramification.

Spring foliage:

Fan and bar branches:

Front - Trunk with Split Base:

Side View (trunk leans away from viewer)

There are design questions to deal with but an understanding of branch development and growth seems a priority. I would appreciate any and all thoughts.