You might want to check out
PickupContainerItem().
You'll have to apply the sort in multiple stages since the items will become "locked" once you attempt to swap them. The swapping itself doesn't actually occur until the server responds. When doing each pass, you can keep track which slots you've put into a locked state and work on the others simultaneously. This'll make the overall process quicker as waiting for the server to catch up can consume a lot of time.