One more thought:

One source of confusion might be the idea that accounts B and C need to be setup through POP or IMAP at all. They don't, and should be set up as Google accounts. You go to Settings > Accounts > Add Account > Google (not "Personal (IMAP)" for example). Enter your gmail address for account B or C and the password and you're set.

Now when you go into the GMail app, swipe from the left and at the top you switch to the new account. After that, you'll have an option for "All Inboxes" that will display a unified inbox.

You can also create GMail widgets on your home screen that will take you to a specific account's inbox or any other label.

This process would, however, require that you stop checking B and C via POP from account A. You'll be seeing double, otherwise.

*edit*
Of course, before following the instructions above, you'd want to remove the old entries for accounts B and C.