It's served me well and it's a 100% free. Get one before it goes lavabit.

https://ruggedinbox.com

I think it will be impossible to get rid of this problem completely. As an option only your own mini server for mail. Only so, otherwise I do not see reliable options. Mail address is now a valuable resource. For example, some lenders order parsing of email addresses and make their base of reliable borrowers. I would make several email addresses for different purposes.