I tried creating the whole page with each of the four lines in a different part.
In this method removing barlines resulted in Dorico adding implicit rests, because the option to show rests in empty bars doesn’t apply. (The lengthened bar has notes in it.)
So I still needed to keep the barlines and hide them using the method recommended by fratveno.
The four part presentation has the best note alignment but has a system barline at the start of the system.
Is there a way to hide that, or at least remove the joins between the staves?
Presenting this in two systems systems seems to be the best way so far but there remains some misalignment between notes in the first and second systems.
This result is good enough for my purpose. The 4-part presentation would also need a way to increase the separation between the 2nd and 3rd staves. Is that possible?