Custom post type parent page

So i’ve looked all day for this and it doesn’t like permalinks work with custom post type. Here’s what I’m trying.

I have property-listings custom post type.

What I want is for the landing like a blog posts page to display 10 properties per page. So I was thinking a shortcode within my post type. So lets say I do that I want this page to live at http://www.mysite.com/listings/

Then I want to create another for solds and for active listings. I was thinking attributes “active” and “sold” on the shortcode then create the following pages.

http://www.mysite.com/listings/sold
http://www.mysite.com/listings/active

Then I want my actual customs posts under each. for example

http://www.mysite.com/listings/sold/%5Bpost-title%5D/

I would do this by selecting the page parent when I write my post (I hacked it so I could choose my page parent)

But that isn’t possible hey? I have to have a slug and I have to use it in my custom post type?

Kind of makes for bad urls. Unless someone knows how I can best achieve this.

Save me! Thanks