First, if you can't auto-update, try deactivating the plugin. The auto update found 2.02 when I did this.
Unfortunately the best I've been able to do is send Interest information via Custom Fields, so these subscribers will still need to be added manually via occasional search and add operations in the CC backend.
I haven't dug into this further, but apparently we are limited based on whether this plugin using the POST vs PUT method for communicating with the Constant Contact API.
More from CC support:
The designation of which lists the contacts will go into has to be setup in your signup form and the script on your site that accepts the data from your form and submitted the API request has to convert whatever your form feeds it into a valid API request that is structured correctly to add the contact with the selected list membership information, and includes authentication information for the account the contacts are being added to.
This request has to be made using HTTP PUT method to update list membership to contacts already on some of your active contacts lists in Constant Contact, as HTTP POST method request to our API only works to create new contacts, who are not already on any active contact lists in your account.
It would still be very welcome for this plugin to allow certain fields to pass information on which mailing lists the contact should be added to.