How to access "add a card" page in Commerce Card on File?
commerce_cardonfile looks for a 'create callback' from the payment method modules. commerce_authnet does not come with the callback, but this patch adds one:

add_card_on_file-2051357-21.patch

Here is the discussion: https://www.drupal.org/node/2051357

After I applied the patch, commerce_authnet_cim_cardonfile_create() was defined on both lines 760 and 1021. I renamed the latter so that Drupal was happy. Then "+ Add a card" became available on each user's "Stored cards" tab. And... it works! 

Can I get my +250 points back? ;)