I think that one of the most important yet undervalued variables that can influence attachment style is general exposure to events. I would argue that most children who can deal with any sort of adversity will benifit from experiencing many different types of situations.
Instead of constantly guarding and coddling an anxious child so that they are always comforted as soon as they are anxious, it seems far more benificial to healthy development if that child is put into various situations. These could be as simple as going to the neighborhood park, and as adventurous as taking the child to a foreign country. If these situations are built up, I believe that even a very anxious child can achieve some measurable degree of comfort in new environments and with new experiences. In fact, to develop a healthy relationship to outside stimulus, I believe that it is essential for a child to be exposed to various environments.
I completely agree with your suggestions, Canute. I think what may be the most important aspect of your ideas would be social exposure. A child may benefit from early exposure to social interactions with peers because such interactions may reduce many of the social-psychological maladies that are common. Moreover, the child would be able to gain knowledge/skills from individuals other than family.