I don't think they really divide their material that way. I don't think any material would be off the table, either for another major look with someone else, or carrying over mostly as is. I think only overall direction determines that sort of thing. I'd think any song, any riff, any chorus, any lyric would be forever fair game, always evolving. Only the extremes would be ruled out of any particular project. I mean, they drag stuff over from years ago, albums ago, all the time.
Using Every Breaking Wave as an example of a complete song - they seemed really confident with it when it was held over from No Line as the centrepiece for SoA. So confident and seemingly 'happy' with it, that you'd have to think it remains to be almost a certainty for whatever comes next. I don't think they would either (a) not give it another look with DM just because it was previously 'Eno/Lanois' material, or (b) if they are really happy with it as it is (was) in it's Eno/Lanois form, I don't that would rule it out of contention for a mostly DM produced album. I don't think they would have a problem with 'offending' Eno/Lanois by scrapping their version and going with a DM version, and I don't think they would have a problem 'offending' DM by nudging a track or two produced by others onto 'his' album. Their history shows they have no problem pillaging the past regardless of the who and what involved, and that they're not at all afraid of a mix of producers and thus sound and feel on any one album. I would not at all be surprised to find the 'DM album' is actually only about 80% exclusively him, in one way or another. Or that the material on it originated from all over the place, many other sessions with many other people. Same as with almost every other U2 album.