I see we're already working with you via our support Live Chat, so we'll just continue the discussion there. Here was our reply in case anyone else happens across this thread:

A "504 Gateway Time-out" error means our Shops server has more traffic demand than it can handle, we now have better automation to detect that condition and reset idle connections to restore access, which usually resolves the problem automatically within a few minutes or so of it starting. This should be cleared up by now.