So I've been communicating with the Maltese embassy in Washington DC (as I live in the US) and I'm going ahead with the citizenship application. I was able to get my Maltese birth certificate by applying online.
Because I was born after 1964 I have to provide a shit ton of documentation such as my birth cert, my marriage cert, my fathers' birth cert, my paternal grandfather's birth cert, my parents' marriage cert, my paternal grandparents' marriage cert etc. All of this is in case I was born outside Malta, which seems a little redundant given that I was born in Malta, but my experience of immigration systems is that they list the hoops and we jump through them.
I also have to prove I've lived outside Malta for at least 6 years as I'm applying for dual citizenship.
They are quite helpful - they have a standard email they send you that outlines the process to go through. You send off all the docs for citizenship, and they go off to Malta. It takes about 6 months to get citizenship.
They also sent me the info on how to get the passport once I have citizenship, but it's so far away I haven't even thought much about it. But I will have to go to the Embassy in person to get it.
Anyway, my advice is to ask the Embassy if you have questions.