I was able to regain access to my phone by temporarily disabling 2-factor authentication.
I switched the NFC Ring Unlock app to "disable." I'm not sure what changed, but after some time and a few unlock/relock cycles with the NFC Ring Unlock app disabled, it has re-enabled itself, with the same symptoms as previously. After getting back into my phone by disabling 2-factor authentication a second time, I checked and discovered that the NFC Ring Unlock app was still disabled, but was overlaying the unlock screen anyway. Admin priviledges were enabled all the way through this process.
I have now uninstalled the NFC Ring Unlock app, since it seems to be too unstable for regular use.