Right, so those are related and if you want different layouts for different views you might need to get creative.
One option could be to use the default event templates (ecp-page-template.php and ecp-single-template.php) and tweak them so the share the style and appearance of your theme – you could then either make one a two column layout (ecp-page-template.php) and the other something else, or, you could even make it so that a completely new template (ecp-two-column.php – you could call it whatever you wanted) loaded instead when certain conditions are met, such as it is an events page and also an archive page.
Does that sound like a workable plan here?