How to deal with 3 months notice period after clearing all interview rounds?

In order to get shortlisted I initially stated my notice period as 2 months. I have cleared all rounds and now I have a call with HR to discuss comp and notice period. As of now the HR has my notice period info as 2 months and I plan on stating that as the offical Notice period whenever asked until I get an offer letter in hand. However after I put my papers in my current company should I
A) reveal after a couple of days to HR saying that my manager usually agrees to 2 months release but for my case he is insistent on 3 months as I have more responsibilities to transition OR
B) reveal around the middle of the 2nd month in notice period that initially my manager agreed for 2 months but since I was the POC for a lot of projects it will take 3 months for transition

I'm just worried that in case A they are more likely to rescind the offer while in case B they have already invested a month of time for my joining so they will likely roll out another offer with changed joining date