Update: It didn’t take long to make the changes Google requested (see comment: The plan for K-9 Mail 6.200 - #11 by cketti). And after a few more very frustrating email exchanges they seemed to be satisfied with the video of the app they made me record.
Then they requested we “whitelist [their] test account” 
so they can test the app. I resisted the urge to tell them (again) that the app is connecting to their service, not ours. But I figured they actually need the app and sent them an APK for testing. They acknowledged that they received the APK on Monday. I assume they’re very diligent in their work because I haven’t received any updates since then.
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