If those cards were suspended, encoded, foretold, or linked to some other ability or effect, they are no longer suspended, encoded, foretold, or linked. If it was haunting something, it is no longer haunting anything. If used in response to a madness ability, then that card cannot be cast, since it is not the same object that it was. If it could be cast using rebound, it can't rebound.

I think a better way would be to actually move the objects to a different zone and back - that way there is an actual reason for each to become a new object.

I think that is unnecessary; rule 406.7 already says they become a new object, and the things that it does due to this are already many things (I listed some examples).