Ah ha. Apparently Twitter only exposes the last two years of tweets via the (non-Premium) API. I knew there was a limit, but I thought it was "most recent N tweets" and since its own website was showing no tweets I figured it was a database reconciliation issue.
Which means I guess I need to modify my script to use the downloaded archive to retrieve each tweet's data individually (which still works; the two-year limit is for timeline requests) and then delete it. Cool.