In the Listings template, how do I force a custom field to show in its own column, rather than let it sit quietly underneath the Title of the record?

A picture might help here

 

 

I should add, it would be nice for the field's title to appear as the actual permanent title of that column, with the field's changeable content underneath on each row. Is this possible?

You would have to completely rework the listing template. There is no easy way to achieve this otherwise. The default listing template just delivers this “forum-style view”.