"To me, a naturalistic look has upward curving branches like it is now and a traditional look would have the bracnches wired out more flat. I was wondering too if the branches would need to grow out longer in order to have proportion with the fat trunk. Judy, with cork elms the bark at the base is the nebari. So, what you see is the nebari. At least that has been my experience. "
As was said, upward pointing branches are a sign of a juvenile tree, as are long thin branches. What would work with this tree is clip and grow. Allow branches to extend and thicken until they are very fat at the base, prune the back HARD to within an inch to half inch from the trunk, repeat procedure successively with each flush of new shoots--you can also use directional pruning and some wiring to push movement into the shoots and branches as you go. The repeated grow out/prune back technique is extremely effective with elms as they grow very very fast and produce extesive back budding. You will build up ramification on gnarly looking branching in only a few years.
This isn't the "wire and be done" kind of design that's used on evergreens. Building believable branching in deciduous trees can't really be produced adequately with wire alone. It's all about the pruning.
A trunk like that deserves branching that matches it.