I believe I found the source of the issue. It is the do_home() function in the breadcrumb_navxt_class.php file. There are 2 sections of the code that is adding a crumb for the post type archive. The specific cases are:
else if(isset($type->post_type) && !$this->is_builtin($type->post_type))
else if(isset($type->taxonomy) && !$this->is_builtin($wp_taxonomies[$type->taxonomy]->object_type))
In our case, the custom post types we created did not have an archive set up when the CPT was created (i.e. has_archive = false). We have a page in our system that has some content on it and then the list of the posts of our CPT. This page is set as the root in the options for the plugin.
Since the code for the plugin is not checking if the CPT actually has an archive before including a link to the archive, that is where the double crumb issue rears its head. The same thing happens on the taxonomy page for the taxonomy for the CPT.
I tweaked things on my local copy to check if the post type has an archive. If it does, then it includes the crumb; otherwise it skips it.
Have you set a release date for version 4.0 yet since you won't be releasing a bug fix for 3.9?