Omit Position Column?

There is nothing built-in to the plugin to allow you to remove the position column. That would be a feature request.
However, if you use a shortcode with the position specified (instead of using location the way you did), then the position column will not be shown.

If that doesn’t work for you, you can use the dataTables extension here:
https://stephensherrardplugins.com/plugins/pta-member-directory-datatables/

That extension gives you a much nicer table presentation that also has a responsive display option for smaller mobile screens, and there are other options that allow you to group by position, or to allow you to remove the position column completely. Note, however, that the settings for the dataTables view will get applied to any member directory table, so you wouldn’t be able to have one table that shows positions and one that doesn’t.

Alternately, you could use some custom CSS styling on that page to hide that column header and the associated td cells.

Thanks for the prompt response and helpful suggestions. The dataTables extension won’t work for me if it is applied equally to all member directory tables, but the CSS styling suggestion may work with something like:
<style>
tr th:nth-child(1),tr td:nth-child(1){ display:none; }
</style>
This works where there is no rowspan, but omits the 2nd column following a rowspan — I am sure there is a way around this, so I’ll keep trying!