Trunk thickening does not come from a shallow container. Shallow container may help produce a shallow root system but not always shallow enough for a bonsai pot so you will still need to root prune at some stage.
Thickening comes from growth above any given section of trunk so allowing lots of growth is the best option to hasten thickening. The other key to thickening trunks is patience. You've only had the tree a few months. I've been growing some for 10 years and more to develop the trunks I want.
Basal flare is one aspect of trunk thickening. Dawn Redwood do that very well when allowed to. I've found that basal flare is directly related to strong, radial surface roots in all species I've worked with. To help with that I'd be unpotting at the appropriate time of year and pruning the roots aggressively. Remove ALL roots growing down as short as possible. Then shorten all laterals which should encourage them to ramify. Encouraging the laterals while discouraging down roots not only prepares your tree for life in a bonsai pot but also encourages basal flare. After a couple of rounds of such pruning the trees seem to settle down and rely on the laterals and grow very few down roots.
Thick branches seem to be a feature of trees grown fast for maximum thickening. The cure is to remove the thicker branches. Most trees will grow new shoots from the base of pruned branches allowing you to grow new ones in a more controlled way.
You will also need to reduce the main trunk at some stage to add some taper. At the moment your tree has youthful characteristics - tall, skinny trunk with no taper. Producing a trunk with taper gives the impression of a much older tree.