imo: The left side (shorter side of fork) in the 4th picture down, could be properly cut off considering it's still young and developing. I agree the tree won't be 'vase' shaped for long if the competing leader is left to grow at will.

Zelkova aren't fussy about the time of year they get pruned but now is a good time as it will have the whole season to work on encapsulating the wound.

Most any zelkova is destined to have oodles of forks -- that's how they grow. You'll have an unending fight w/it to get rid of them.

The need for pruning any young tree is debatable, especially one that is growing out in the open and has a decurrent growth habit.

I've 'structure pruned' many maple trees but after a point, they're generally 'on their own'.

:-)

Well I'm getting the impression that this is just the way this type of tree grows. If that's the case then I'll just let it go as is. I don't see any reason to fight against the way a tree naturally grows.

Well, it's not a bad idea to do structure pruning on a young tree, to give it a good start.

I generally structure prune all my newer trees when they are smaller so they start out with as good of form as I can get, before they're too big to mess with. Maybe that's just me.

But in no way would I continue structure pruning on a tree year after year, that's just too much work and unnecessary in most cases. :-)