With the release of 17.10, everything broke because Wayland was bought into replace X. With 18.04, wayland is out again — something which I am pretty glad about, because in my experience it was pretty unstable, with the desktop crashing out to login fairly often.
The 17.10 solution appears to have been:
gsettings set org.gnome.desktop.peripherals.trackball scroll-wheel-emulation-button 8
This fails again on 18.04. Fortunately, the solution is quite simple which is to just return to the libinput configuration that we had before.
xinput --set-prop "Logitech USB Trackball" "libinput Scroll Method Enabled" 0 0 1 xinput --set-prop "Logitech USB Trackball" "libinput Button Scrolling Button" 8
I look back to the good old days of gpointing-device-settings which uses to work and looked nice. Why have we come so far from here?