You are mistaken.
The NMS (i.e. AOA) match does not make any mention of whether or not those individuals participated in the NRMP match. All it states is that 824 individuals failed to match in the NMS match.
As I mentioned above those individuals either (1) only ranked their top AOA program because their next ranked programs are ACGME, (2) applied to a competitive AOA field and a non-competitive ACGME one so they are using the NRMP as a backup match, (3) failed to match AOA, but also applied ACGME and are waiting for the NRMP match, or (4) just applied AOA, failed to match and likely scrambled post-NMS match.
Some of those individuals that are participating in both matches will have failed to match AOA and then failed to match ACGME. By you counting every DO that failed to match in the NMS match and adding that number to every DO that failed to match in the NRMP match, you're counting those people twice. In addition, you're counting people that failed to match AOA, but subsequently matched ACGME, in turn further inflating the number that you claim need to scramble.
You are able to participate in both matches as a DO. The AOA match occurs earlier, so as a matter of strategy, many people will apply to both types of programs, and use the NRMP match as a backup. They can do this by applying to a competitive field in the NMS match or by only ranking (similar to suicide matching) their top choice in the NMS match, knowing that the rest of their programs are in the NRMP match.
As far as the SOAP, historically 100-200 DOs manage to find spots in it each year, so that still usually leaves 500+ DOs that scramble at the end. Most are able to find spots, which is why DOs have a national GME placement rate of >99.5%.