At Will Employment and Notice Period IB -> PE

I want to leave for a PE gig the moment my next IB bonus hits my account, but my current employment agreement stipulates a 30-day notice period. Ordinarily I think there wouldn't be a problem, but the PE firm doesn't want to buy me out and my firm (BB) does not want to work with me - I get bonus paid end of August (but communication day is end of july), months after the intended aso program start date. Additionally, 30-day notice period stipulated in current IB employment agreement pushes my nearest possible start date to a pretty unreasonable number of months after the intended PE aso program start. I am worried about not being bought out so I can start early / on-time and being told I need to begin on a date that would either preclude me from collecting my IB bonus or not acknowledge my full garden leave period.

Obviously, my current IB employment agreement is the standard at-will employment. There is even a clause indicating I can request for the notice period to be reduced and the firm at its sole discretion can agree, implying the 30 day period is flexible. So my question is, in the worst scenario, can my current firm actually legally enforce even a single day to serve my stipulated notice period and prevent me from joining the PE firm given I'm employed at-will? Are there actual consequences if I resign and do not serve the garden leave period even if the bank tells me I have to?