You are correct. I'm checking around and can't easily find a free provider of anonymous email service.
How about this solution?
1) Get your own domain name and pay the fee for a private registration. The total cost should be less than $20/year. I recommend
Godaddy for registering domain names.
2) Add an email address within your private domain as an extra "Send Mail As" address in a free Gmail account.
3) Use the Google SMTP servers (not the webmail interface) for sending email.
An alternate to 2&3 could be launching a tiny instance within
AWS, installing an easy to use control panel, and allow authenticated smtp relay for your new private email addresses.
One way or the other someone is going to have some billing details about you
Since it sounds like masking your IP is only an occasional requirement, what about getting a domain name, making it private, keep the email hosting with the registrar used to buy the domain, and then driving to the local coffee shop with free wi-fi when you want to send an email and not have your home IP address associated with the email?