Update: BioShock is no longer region-locked for Singapore.
Original: The solution to get BioShock 1 unlocked from the Steam BioShock 2 pre-order is so easy, it makes me wonder if we are all idiots for missing out a simple, additional step during the gifting process:
Step 1: From Steam, click on “Games > Manage Gift Passes”
Step 2: If you have pre-ordered BioShock 2, you should see BioShock 1 under your list of gifts. Select BioShock 1, and click on the Send button.
Step 3: Choose to send your gift via e-mail. Key in your own e-mail address.
You are essentially gifting the gift to yourself.
Step 4: You should receive an e-mail from Steam informing you about the gift you have received. Open the link provided in the e-mail, and BioShock 1 should be added to your games list.
Step 5: Enjoy playing BioShock 1!
The author wishes to thank dKiWi for figuring out the solution to this whole mess.