To get a Let's Encrypt wildcard cert, I ended up running my own DNS server with dnsmasq and delegating the _acme-challenge subdomain to it.

Pasting a challenge string once and letting its continued presence prove continued ownership of a domain is a great step forward. But I agree with others that there is absolutely no reason to expose account numbers; it should be a random ID associated with the account in Let's Encrypt's database.

As a workaround, you should probably make a new account for each domain.

You bothered to manage your LE accounts? I only say because when using the other two challenge types with most deployment scenarios you were generating a new account per cert so your account ID was just a string of random numbers.