Ruffled 29-2264 was changed in 2002, most likely in part because of the Spady case, to limit the set aside. This was again edited in 2005 to further emphasize this limitation. Having a conviction "set aside" now seems to only include the restoration of voting rights after 2 years, for other civil rights you would need to go the pardon route. Since this is newer law it over rides the older portions that you are quoting from section 4.
But for the purposes of this case the conviction was set aside before this change so his rights should be restored, but with the confusion created by the changes and when they happened it will need to be reviewed carefully by the prosecuting attorneys office in discussions with his attorney, and may even require a formal opinion from the AG's office.
It's all still law. There is no conflict. Section 1 doesn't say that a pardon is the only way to restore some of your civil rights.
Since section 1 says that your right to vote is restored 2 years after the completion of probation when a conviction is set aside, and that "other civil rights" are restored by the pardons board, then that would be interpreted as the only right restored by having a conviction set aside is the right to vote since there is a different method provided for the further restoration of rights. I will note again that this would need to be reviewed by the Supreme Court, and does not apply to the case at hand since it was set aside under the old law.