The EIR will be sub-ICAO, as will be the LAPL.
Not sure how this will be handled. The EU could force member states to file differences to ICAO on this, or they could do it individually. If this were done, then these papers could be valid worldwide unless specifically objected to by the airspace owner. But I suspect nothing will be done because, in general, Europe is big enough to fly around and flying outside Europe is a big logistical hassle (avgas, etc).