Social security number is step 1? Then you likely have bigger problems then your gmail. If your in a position that this actually is a big problem, get a private email server and gpg.
It's a password that you reuse everywhere and never change.
"The SSA may assign a new Social Security numberto you if you are being harassed, abused, or are in grave danger when using the original number, or if you can prove that someone has stolen your number and is using it."
Unfortunately, maintaining and securing a private email server can be a big job. Google already does that job, and their data centers are much more secure than the VPS provider where you'll host your private email server.
All I'm asking for -- and I don't think this is unreasonable -- is to rely on their world-class technical security, while being able to disable all password recovery methods, which are vulnerable to social engineering.