Autoforward everything you get to it to one of your custom domain emails, and set up an autoresponder that says you're no longer using GMail, points to your new email, and tells the sender you'll stop checking GMail soon?

After about a year or so of that (plus having the presence of mind to update your email address whenever you use a service), you should be able to delete your account without too much inconvenience. Yes, it's a pain, but that's how lock-in works.