Wow, a lot of useful info in this thread - a rarity on RS!
I'm in the same boat - dad was born in HK and I was born here. I got a HK ID card a few years ago (with parents). Then in October of 2006 I went to HK again with my parents to apply for the "smart card". The smart card wasn't ready until a few weeks later so my dad went to HK again in Nov. to pick it up for me.
You'll definitely need to go with your parents, or at least your dad. Yeah best bet is to call up the embassy. You're definitely entitled to one though.