This is not as straight forward as you would think and can give you some headaches. You will need to make use of rewrite rules to rewrite your desired URL.
The real problem here is that property/map/ will be treated as a single post, which will 404 because a post with that name does not exist. You will need to tell WordPress that whenever it encounters this specifc URL, it must treat it in the same way as a normal custom post type archive page. I can’t help you with rewrite rules as frankly, that is a specialized section that I still need to explore and get to understand.
Just to give you some idea, you can go and check out this post I have recently done. You must also check out the linked question in my answer and check out the answer from @Milo. You will need to do the same type of thing, rewrite your URL to the home page with your custom post type, and then set your conditionals accordingly.
Once you get that part going, then it is easy. You can simply then just get the URL and if it matches your URL, you can use the template_include filter to tell WordPress to use your custom template.
I believe that the linked post will solve almost all of your issues.