Since filters are specific to the Web mail system you may or may not be able to fix this.
Most folk I know just learn to move and send out a final email to everyone that your new email is now "Heyit's me @ nmynew.com"
I see more and more folk ditch classic email apps like Thunderbird for web mail. Or a smart phone.
My first email was a Verizon email that my parents set up. It has been annoying to use it now because Gmail's interface is better and most people don't use Verizon's email system. I already gave my Verizon email to my contacts, so I decided to merge the emails together. I went to Gmail's settings and made it so that all of my Gmail email will get sent to my Verizon email. It said that for me to do it the other way around, I would have to go to the other email provider and do what they say. But then I realized that if someone sends me an email to my Verizon account, it would go to Verizon, then to Gmail, and when Gmail receives the email it would go to Verizon, and then to Gmail, and so on, giving me infinite emails. So: Would this actually happen, or is Gmail/Verizon smart enough to prevent it? Is there some solution with filters I can use?