That's the thing - I can't. My oath is next week so let's say I manage to expedite certificate and get a Canadian passport by Dec 1st week/2nd week. If I initiate the OCI, I won't have my Indian passport with me by Jan 8th (Nexus appointment) So I need to wait until I get my Nexus interview is complete before applying for OCIThe processing times for surrender were updated to minimum 8 weeks for Toronto jurisdiction the last time I checked. So, expect it'll take at least that long for you to receive the cancelled passport.
Once you receive it, you can take both the cancelled Indian passport and the Canadian passport and complete your interview.
OR
I inform CBP that my Indian passport is cancelled and I don't have it and just proceed with Canadian passport.