The other argument I have seen with this is that extra copies of DNA segments are "stored" DNA for future use to be brought out when needed, even if they have to be combined with segments from other "stored" DNA to make the necessary new genes.
Indeed. This argument generally revolves around the non-coding regions, tandem repeats, etc. It often takes one of three forms: a) the non-coding regions are "storage" for DNA material that will be incorporated into exons when "needed" (this is the teleological IDist formulation); b) it represents the remainder of the universal genomes present in the various "kinds" before the Flud, and hence are the bits that weren't used up in the hypermicroadaptations experienced within "kinds" subsequent to that event (and also represents the bits that are available for shuffling about when any new adaptation or species is identified, thus bolstering the "no new information" argument); or c) it represents an "echo" of the perfect all-encompassing genome present in the original organisms of the GoE before the Fall, and thus is evidence of the long-term degradation of all life after the apple incident.