In your scenario, there’s practically nothing that can be done. If a service that you rely on goes away, you’re basically out of luck. There really isn’t any protocol or particular leverage that you or I might have to do something with a company, website, or service that disappeared.
But I do have some suggestions on what you could do.
If you haven’t tried it yet, I would check the Whois record. Whois.domaintools.com is one service that I frequently use to look up Whois records and see if there is a contact email. That way, you can email them and see if they will do something.
My guess is you’ve already done this, but I want to mention it, in case you haven’t.
Email your contacts
Because people are still sending you messages to this account, email them and tell them your new email address. If you have notifications, newsletters, or other services that you signed up for, go to their website and change your email address with those services.
You could also go so far as to set up your own automated response.
Set up an automated response
If your email service allows it, set up an automated response. When someone sends you an email to that old address, you can set up your email to send a response along the lines of, “Hey, this isn’t my email address anymore. Please use my new email address.” Whatever message feels comfortable to send to people who might still have your old address.
That’s basically setting up your own bounce message, which is probably better than the alternative anyway. If the old email address goes away and the service starts bouncing emails sent to that address, their messages are likely to be much more cryptic and can’t include your new email address. Your auto response is probably going to be clearer to the senders than any automated bounce message would be.
Get your own domain
You’ve finished with what I think is the best solution: getting your own domain. As long as you own your domain, then you can have any email address on it. Keep it as long as you want it, using whatever email service to actually handle the email you want.
Ultimately, when it comes down to a service like this going away, I don’t have any magic answers for you. But I do have to say that I find it incredibly ironic that a system whose business name is Forevermail has gone out of business. It clearly wasn’t forever!