The very next day after this, I went and got myself a “proper” ball joint separator. It was the right thing – did the job in a matter of minutes. Didn’t even have the time to make tea.
The other end of the rod had a torn boot, so I took that off, too. Again, without tea.
Here’s how it looks.
The separator is made of pretty good steel, and the pushing screw has a ball joint of its own, to reduce friction while turning. If you intend to make one, take these factors into consideration.