That looks like a business Hotspot so I am not sure Cox has permission to reset the modem as that would affect the business service. Try emailing Cox at firstname.lastname@example.org with your account info and link to this post. Worse they can say is no. Good luck.
Seems like a security loophole to me. Some camera systems are cloud based and require a internet connection to record or atleast view remotely. If I had a business, I wouldn't want someone resetting my gateway without my permission. Why if I am in the middle of a big download? Do they at least wait until after business hours? Then again maybe that is just even more of a reason not to use Cox equipment.
More on topic, how do you reach "Advanced Support" now? I have heard from Reddit that the phone support is (atleast) partially outsourced and escalation is difficult.