I hardly understand your problem. You cannot have the same user name with the same popname ?? It will be one unique mail address, no?
In Thunderbird with Avast I have for account parameters

  1. server name: 127.0.0.1
    2.username: myself#pop.mail.com

So, you’ll have to create different account that will be different in the username (myself#pop.email.fr, myself#pop.mymail.com etc…)
I suggest you to import the accounts without Avast configured in OE then reconfigure the accounts for Avast in Thunderbird (I hope you have not thousands of accounts).