I don’t have time to properly look into the examples you’ve been posting, but I just want to say that the unification machinery should not need to do anything special to work with logical-or, append-list, etc. They are defined in just the same way as any other type. (If the problem really is to do with the unification machinery, then interactive unification should give the wrong feature structure.)
Have you checked the value of deleted-daughters? (see here)