Thanks, yeah I had run into that particular issue previously, but it has been sorted out in this case.

It turns out that the issue seems to be the same one that (at least according to the Internet) causes most problems like this - the EmptyPoint colour needs to be set to something other than Automatic. When this is done, the data series lines appear ... but all in the same colour. There are workarounds, and I guess I'll have to investigate those.