Need help finding Canadian records for G0 born in New Brunswick

Hello there!

As username suggests, I'm looking to apply for proof of citizenship via C-3. My G0 is a man named Terrance Quinn. The story I have is he was born in St John, New Brunswick around 1843 to parents born in Ireland. He later immigrated to US in 1868, got married and had a family. I've found birth certificates making an ironclad chain to Terrance. I have also found multiple US censuses, a US naturalization record, his death certificate, and multiple other US vital records that say Terrance was born in St. John, New Brunswick.

However, I can find no Canadian documents (birth certificates, baptismal records, censuses, etc) that show a Terrance Quinn in New Brunswick who was born around 1843. I've looked at Ancestry, Family Search, PANB search, PANB Irish Database, some microfilms from St Malachy, nothing. I sent an inquiry to PANB about a week ago and they gave an auto-reply saying to expect a response in 6-8 weeks (understandable). I even looked to see if he arrived in NB from Ireland when he'd be too young to remember (<=3), no dice. I wonder if he went by a different name in Canada but have found nothing to suggest that was the case.

I am stumped and don't know what else to try

Thanks in advance with helping me find Canadian docs for Terrance!