It sounds like you've come across a situation where either the travel agent or SQ hasn't recognised that Frank is a shortened form of Francis, and they're looking for too literal a match. That said, your birth certificate plus the death certificate sounds like it's sufficient, and to be honest I'm surprised the airline is even prepared to countenance an obituary report - which is in no way verified by anyone prior to print - in the first place.

In terms of your refund, I think we can be sure that it's going to be a lot more than the $35 it's going to cost you to get a replacement birth certificate. If you half the total fare you paid you're not going to be million miles out. I'd also say, as others have hinted, that in securing a refund on what was very likely a entirely non-flexible ticket, you've actually got a very good result. It's not one I'd be complaining about too loudly.