Different Posts Pages, Same Custom Post Type, Differentiated by Custom Fields

Site in question (specifically this event page):
http://raveisking.danconia.us/event/

So I am attempting to create a blog that does previews and reviews of musical works and music-related events. I am specifically having issues with the events area. I have created an “event” custom post type which has several custom fields including a “start_date”. I want to use this “start_date” custom field to automatically have the server split these post types into future and past events (by comparing with current date / time).

The URL post above specifically shows future (upcoming) events but now I am wondering what would be the best way to create a similar page displaying previous events? And how would I attach it to a specific URL?

Currently I am attempting to create a page template for past events and replacing the main query & loop inside of that page but when I create a page-event-review.php and put it in my child theme folder the option doesn’t seem to show up as a template in the page editing area (“Page Attributes”).

I should comment that I specifically do not want to have to mark events as a sub-type individually… I really would like PHP to figure out for itself whether the event started in the past or starts in the future and divide the events as such. What is the best way to move forward with this?