I'm posting this as a separate topic. The problem proved definitive; I had to do the conversion using OpenOffice in 13.1. When I tested the conversion in LibreOffice with a tiny file with no tables, pictures etc, the conversion worked fine.
This is presumably a problem with LibreOffice, and also something that isn't going to happen with every file. Nonetheless, I can't recall anything of the sort occurring with OpenOffice.
It's potentially a very important issue. My clients aren't likely to listen to me if I ask them to install an open source office suite. In practice, the ability to convert to proprietary file formats is essential.
This was a file containing around 15,000 words, with one small image file, and a massive table in the middle.

