So regular pruning will cause the branches to back bud, thickening the canopy?
Proper pruning will create ramification, which will create more branches and more leaves, making the canopy fuller.
I keep seeing different advice for maintenance pruning Chinese Elms, some saying every 2-3 months and others saying 1-2 times a year. Would you be able to clear this up?
Hmm.. not too experienced with Chinese elms. I prune the first flush (when it has hardened off), then I prune again when new shoots have fully grown, if / when needed. I do not prune where I need more girth / longer branches etc.
And, should the top + sides be pruned more often / vigorously to ensure even growth?
No, you prune where and when it is necessary. Depending on the shape of the tree, you will let a branch / branches grow freely to get more tapering,
You may want to let branches grow freely to develop them, then cut them back, let them grow again, also to get tapering.
A bit much to explain in a forum post; keep studying, there are many sites with in depth information.