This is exactly why I change email addresses every 1/2 years. I've forwarding setup from 3 of my old addresses to my current address and for all financial transactions I only use my current email address.
Using mutt or offlineimap:
1. Configure POPS/IMAPS access to the account, use Maildir format locally.
2. Download all messages.
3. Copy your saved messages to another location.
4. Delete all email on server.
Local search tools can then be used to access that archive.
Almost all of my conversations are over chat and my primary usage of email is to sign up with sites or receive updates on my orders on Amazon/whatever. I haven't felt it as a curse so far. YMMV