Background
I've worked with my current employer (Ontario division of a large tech company) for about 5 years now. For the past 5 years, I've been in a "senior engineer" position, but for the past 24 months, I've taken over for the "chief engineer" for the division, and routinely take over for my manager (he was promoted, and his old position was never officially replaced, so I'm basically working 2-3 paygrades above my own, but my employer has never corrected this). I do great on my KPIs/performance-reviews, and my employer keeps promising a promotion and pay raise every 6 months that never comes. I've communicated my dissatisfaction bluntly on this topic several times, and no changes have occurred, so I successfully interviewed at another tech firm (not a direct competitor), and managed to negotiate a better position, title, 45% pay increase: yay. The catch: I requested a 2 month delay (rather than the 3 weeks notice my contract stipulates) so I can have some downtime to recover from burnout. The job offer is signed and countersigned, and I've already cashed the signing/onboarding bonus cheque I negotiated.
Problem
Something was very weird about how my managers acted this past Monday, as I'm suddenly being called into meetings on the "importance of the project I lead", and I've received two requests to sign some paperwork (which requires me to come sign in-person on-site, and I can't have a copy myself) that would make me agree to have "fiduciary duties" and a 3-month severance/notice period in place of my 3 week period. I flatly (and politely) declined, as "I'm not an executive, and I'm sure not paid like one, so this fiduciary duty request seems wildly inappropriate, and I won't be signing a thing." Something smells fishy.
My employer has requested that I focus on training more people to be "experts in my technical domain", but is getting angry when I insist the individuals will need to learn a lot of new topics first (i.e. master Linux kernel development, learn Linux security and firewalls, etc.) before I can teach them the advanced topics, and my employer is all but accusing me of being "needlessly difficult".
Question
Should I just give 2 months notice to my employer? I only legally owe them 3 weeks, and they technically "get their way" with a greater notice period for which they're pressing me. Ideally, they just send me packing and pay me severance for 8 months, but I'm not sure if they can reduce the pay to just 3 weeks if I've already handed in my notice. This is in Canada, as noted at the top.
How should I proceed? Provide 2 months of notice, or just wait a few weeks and hand in my 3 weeks notice when I'm 3 weeks from starting my new job?
Edit: I can live without the excess downtime more easily than going 5 weeks without income. My primary interest is making as much money over the next 8 weeks as possible, be it from either regular pay from my current employer, and it'd be awesome if they felt compelled to fire me without cause and pay out my severance (8 months of pay), but I don't want to miss some loophole and get fired and only be paid 3 weeks of severance.
Thank you.
Edit: the solution has concluded a lot sooner than anticipated. Thank you for the advice.