I am so, so sorry, mumofbeautys. You and your twins are incredibly brave. Of course, you are not being unreasonable for being angry and upset with this situation.
We know and understand that it isn't the individuals themselves (who weren't on the donor register) that you are angry with, but with a system that leaves your daughter waiting in such a precarious position.
You are correct when you say that many will have their reasons for not signing up, and who could ever argue with those reasons, but a lot of people won't have signed up because they haven't got around to it, or they need more information, or they're not sure if their organs would be of use, or they haven't yet discussed it with their family, or they need their fears alleviated, and so on.
The current system does not address the apathy/ignorance/fear of the majority. In fact the current system barely addresses the situation at all, spending just a tiny amount on advertising, information and promotion.
Now I would never be in agreement with a compulsory system, but can easily visualise an opt-out system (rather than the current opt-in system). Strangely enough, I suspect if we did have an opt-out system the authorities would be so fearful of accusations of organ harvesting and inadequate information, they would suddenly find a huge amount of money to spend on on advertising, information and promotion. IYSWIM? 
As I type this, a wee voice in the back of my mind keeps saying that it only takes one charismatic individual, to get a successful nationwide campaign going _ and you sound lovely mumofbeautys 
(no pressure there then).
Will be thinking of your little girl in hospital, and hope you have time to keep us all informed about how she is doing! 