How to duplicate custom posts as custom posts?

I have a multisite network at

The WMPU Dev plugin, Recent Global Posts Feed was installed in /wp-content/ using FTP upload. Autoblog is installed and activated on the one site where I wish to use it. A third party plugin named Pazzey’s Store Locator is installed and network activated.

I created an Autoblog feed following the identification instructions provided by the Global Posts Feed. The feed is …

I processed the autoblog feed. The only posts that did not come through were the Pazzey Store custom posts. Regular posts from other sites in the network flooded in.

I would like the Pazzey Store custom type posts to come in as Pazzey Store custom post types, so the [storelocator] shortcode will include them in the master store map on the root site.

How I do that?