Howdy Noah,
You could install WordPress and our calendar, choose a very minimal theme, that lacks any information in the header or footer, then you can embed the events page inside of an <iframe> on any HTML page including your site. That should actually work pretty well, but I am not sure if you are trying to avoid running WP altogether. If so, then you are out of luck. Our plugin is inseparable from WP in that it relies on the WP API behind the scenes. But, to the user embedding the calendar in an iframe should be pretty transparent.
Does that make sense? Will that work for you? Please let me know. Cheers!
– Brook