The issue was that the get_previous/next nav filters were “out in the open” in the plugin; so they were executed every time the plugin was loaded. I put them in a function called myplugin_set_nav_filters(), which I invoked before the loop in the CPT single template, and everything worked as advertised.
Now the nav on regular posts is no longer being filtered by the CPT posts; and the CPT page is getting the filters it needs.
I hope this helps someone.