I'm on my last visa (expires next month) from a 1-year multi-entry "O" based on having a Thai son.

A few years ago I got a 60-day extension based on just the birth certificate (my name as father) and a request letter and copies of ID card & house registration from my son's mother (no marriage license). No proof of funds requested.

Will the above still suffice ? I can supply proof of funds (400,000 Baht ?) if necessary. What about requirements for 1 year extension ? Still need a "Bai Rapp Long Batt" (Certificate of Fathership) or Marriage License for that ?

You can still get the 60 day extension with just the birth certificate.

But a one year extension may require getting a court order giving you custody of the child in Bangkok. Some offices still accept only the birth certificate.

60 day would be available but not one year without legal proof of parentage/custody/or marriage.