Answer
This wasn't supported by the Aurena framework as of the point this was checked — custom fields specifically inside this class of data-entry dialog/assistant (as opposed to a regular page) weren't achievable through configuration, even though it was already a known, raised requirement (also needed by the CRM sales process) and was on the roadmap for a future Cloud release. In the interim, it was possible to make a custom field visible within the dialog, but not to actually enter and save a value into it there — genuine data entry for that custom field still had to happen from elsewhere (a regular page tied to the same underlying LU) rather than directly within the dialog itself.