Having resolved my squished projection I'm now facing the fact that QGIS exports all my labels as vectors, which means I can't take the map over to Inkscape and fine tune the fonts without retyping them all. Is there any way around this?
Under Layer Properties > Labels, there's a little button at the top right, hover and it reads "Automated Placement Engine".
One of the options in that dialog is "Draw text as outlines (recommended)" and that does, indeed, export text labels instead of outlines.
So glad I managed to find it.