Neil,
The mistake was done, I know you have admitted it. We had the similar case of pregenancy when medical was requested. We didn't do medical in the given deadline for the pregnant member, got a letter with words of appreciation from CIC doctor with an advice to do it later when it is convenient. (Actually we were really reluctant to leave Europe for Canada, and never wanted to risk baby for XRay)
Later in the passport request we did not get any associated links as you got in your email. That means, they were keeping eye on your pregnancy and let you know by email. That link was case specific to you, which you say you didn't check (which CIC didn't believe).
You have normally 2 months time, but you send the passport hurrily or deperately (probably CIC thinks so).
You didn't think it necessary to inform the CIC though it is strictly required by it from all applicant to inform CIC about change in family structure and other associated factor. (Probably CIC again thinks you did not comply here too).
You later sent the application form even without noticing them. Normally people send a letter (we also did the same) informing CIC and wait for further instruction.
Why I am emphasizing the above points is to help you find a way out. If you see from CIC point they think you didn't comply with the rule, thank god they did not find a point to blame you of misrepresenting.
The OP manual Leon has posted is good for normal cases. That means, it is for those people who respond the issues as per instruction. Now, you have to come to this category.
You got passport request few days before your delivery. A good "excuse" (please forgive me for this word, I guess you have gone real stress and pain during that time) should be that you were near the delivery date and could not check all the links, you were in pain or distress or something.... That is the situation where you were different than a normal healthy person, where mistake or carelessness can happen (A good point to remember when you talk them again).
What I would do in this case is: Try to call CIC, convince them or ask a way out. I have read many instances where the baby is born after issuing visa, the visa is canceled and they include the baby, do medicals and reissue visa for all. The officer saying you to start from the scratch means he is thinking you tried to manipulate them by not following the instruction.
Even ask them if you can land without including the baby, and later sponsor the baby (it is better than start from the scratch). Don't be rude to them on phone. If the things are not going to work then appeal, where it is necessary. But be careful, they don't charge you of misrepresentation. I wish you misunderstood them, and can include baby just as others do. good Luck!