I was thinking in that direction too but right there on page 2 of the syllabus in item (c) is the opening for Arizona to adjust their process and get the form altered.
The NVRA permits a State to request the EAC to include state -specific instructions on the Federal Form, see 42 U. S. C. §1973gg7(a)(2), and a State may challenge the EACs rejection of that request (or failure to act on it) in a suit under the Administrative Procedure Act. That alternative means of enforcing its constitutional power to determine voting qualifications remains open to Arizona here.
Should the EAC reject or decline to act on a renewed request, Arizona would have the opportunity to establish in a reviewing court that a mere oath will not suffice to effectuate its citizenship requirement and that the EAC is therefore under a nondiscretionary duty to include Arizonas concrete-evidence requirement on the Federal Form.
Well, AZ can request a change to the form. Sure Holder will get right on with complying with that request...