There does not appear to be any way to control the sort order via the API, only the parent/child relationships.
It looks like I might be able to hack it into submission by doing what looks to be an insertion sort on the existing items to re-add them to their current parent - at least that looks like it does it in the web UI. That's a horrible hack though.
Suggested possible calls:
and a UI function where I can click on any item in the virtual hierarchy on the rightmost column and then click on a button at the top to put every item under it in sorted order.
Any update on this option? Would also like to have this for the sub-projects tree as well - including a UI element for the same.
Related question - I don't see apiary docs for subprojects when I go to the link. Is that not supported/published?
I have added apiary docs for subprojects. Unfortunately there is no progress on sorting subcomponents or subprojects.