Oh, my goodness. I triple checked everything and still messed up. My apologies. Correct URL and all details in Hidden content. I appreciate your patience.
Incidentally, since this is a staging site, Joomla's default Cassiopeia template is still enabled, but not the default, so you're welcome to test using it.
The steps, just to be clear, are: System -> Site Template Styles (Site) -> shaper_helixultimate - Default -> Template Options. Error occurs on "Save."
Note that the site has several custom CSS files, but we have no problem saving those or working in the "Site Templates" area. It seems only to be with Helix's Site Template Styles.