I guess it's time for an update on this situation, after a couple more calls with HR and my boss last week.
A little background why I didn't just stick to two-week notice from the get go. The MegaCorp I work for is publicly traded, and my role (in finance) could materially impact the integrity of the financial reporting for Q1, so my boss is very worried that if I'm gone before the end of April, the company's financials could face severe scrutiny from auditors. I've been with the company for many years and had great relationship with my colleagues and our auditors. My boss was hired a couple of years ago and that's when my work life started going downhill. But I still feel like most of people I work with are genuine folks and I don't want to make their life a lot hard if I can do something about it. I've left all my previous jobs on good terms, and I would like to do the same if I can.
So after I get my boss and HR to believe that I'm really ready to leave instead of taking a couple years off with plan to return (I'm in my early 40s), they turned around and wrote me an offer. There will be additional compensation through end of April for me to stay until then full-time, while ensure Q1 is done right and I fully transition my responsibilities. I will be on retainer for another several months (for a fixed fee in exchange of few hours of consultations as needed) to ensure they can get questions answered. Although the additional compensation is slightly lower than what I asked for, it is a more sincere offer so I'm glad we finally worked things out. The terms are all written in legal agreements with signatures from HR, my boss and I.
I'll update this post later on to let everyone know how the extra month works out.
Thank you all for very helpful input.