Saving E-mail messages outside E-mail app

My E-mail account was cluttered with too many old messages that I still wanted to keep. They were affecting the viability of that account, so I tried moving them into the Documents folder. That didn't work out too well. Fortunately, I still have them, or copies of them, in my TRASH bin.

What is the best way to keep these messages together in a folder outside of my E-mail account?

I'm not sure if it's related, but the bottom of my MAILBOXES column says "Moving Messages 42 of 295" It seems to be stuck at the point.