Don’t be daft and try to go directly to get_option( 'theme_mods_themeslug' ).

This one’s kind of embarrassing. I must have just not known that get_theme_mods() existed. Whatever the reason, I went straight to get_option( 'theme_mods_themeslug' ); to pull it out. This will work. Until it doesn’t.

When someone creates a child theme, all of your get_option( 'theme_mods_themeslug' ); will still point to the parent theme. That means any settings saved via the customizer will not be retrieved.

So just use get_theme_mods(). You probably already were.