I stumbled upon the answer. It seems that Amazon Linux and Amazon Linux 2 have two entirely separate sets of instructions for installing certbot.
I was using the Amazon Linux 2 instructions at https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/SSL-on-amazon-linux-2.html#letsencrypt when I should have been using the Amazon Linux instructions at https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/SSL-on-amazon-linux-ami.html#lets-encrypt-alami. Trying again with the correct set of instructions got me a working certbot-auto.
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