Yes, James talks of a floating pericope, but it is the theories that are sinking. And yes, James pretends that he is defending Markan authenticity. However, his position is easily refuted by the contras and is a faux authenticity.
Also to be added here. Information about the books by Hester and Lunn, and their positions.
What is not included here is the discussions of particular evidences, that is planned for a separate thread. And there is lots of fine material easily available about the massive evidences.
Specifically on the Snapp Sinking Pericope Theories
Here are some of the discussions to date. The plan is to make them into an article here: