Answering my own question for anyone searching... the lack of responses here and a lot of googling and video watching seems to confirm that you cannot currently drag clips to move them around on the iPad Cut page upper timeline like you can in the desktop version.
So my workaround is to use the unsupported keyboard hack to temporarily reveal the hidden Edit page, go to it, then use the keyboard commands Shift-Cmd-comma and Shift-Cmd-period to swap clips (or groups of clips) to the left or right respectively. Not an ideal solution as the hidden pages are crash-prone (which is why they are hidden) but it does the job.