The answer to the question "who is to determine Catholicity" or enforce discipline is "the bishops."  So, the first step to my thinking would be for the bishops to arrange themselves in a hierarchy in order to get the basic tasks of administration done.  This, presumably, they have accomplished after a fashion.  Other bishops should be persuaded to assist in synod.

The second question that arises from the first is "when did the papacy become vacant?"  Clearly, the pope's existence is not required for the bishops to retain their offices, or act.  Where this otherwise, no bishops would be able to continue in office after the death of a pope, and no bishops would be permitted to create a pope.  Everyone knows that a pope cannot create another pope.  Deciding when the papacy became vacant determines which bishops have a mission that directly traces to a pope and which do not.  

A third question that the essay suggest, to my reading, is "what if the papacy remains vacant for a very long time - for example, generations?"

This, in fact, happened in areas overrun by Muslims in times past, and it happened during the great western schism of the late middle ages.  The function of the Church continued in union with the local hierarchy during these instances, even without the explicit guidance of Rome.  If the papacy is not to return for the foreseeable future, what does this suggest to the bishops of sedevacanist Catholics?  Certainly, it must at least suggest a closer analysis of the second question:  when did the papacy become vacant?  It also raises the question, I think, of how circuмstances could have come to such a pass.  What errors were made, and when, that led the abbeyance of the greatest see on earth?  

Just some thoughts, and thank you for a very interesting paper.  

I don't know, either -- and it was brought back by a person who joined yesterday.

At any rate, it sounds like this thread is outdated and shall be retired.