What is the simplest way to resolve this?
From what I've read and been told the options are as follows.
1) Ask my ISP real nicely to open Port 25. Will they frown on me using port 25 to verify emails? I don't want to get in trouble with them.
2) Find a local hosting provider (again, noob so I have no idea what that is) and verify the emails via web scripts using this tutorial Atomic gave me
3) Use proxies (I'm told this is very expensive for even a list of 10K)
4) Pay someone to give you access to a remote server with port 25 open.
Please explain this to me like I'm 4. I appreciate any and all advice.