You can solve the means problem by making everyone wealthier or by lowering everyone's expectations. The problem is that "how much it costs to raise children" is dependent on your environment. One group's normal is another's neglectful parenting.
The catch-22 is that the people you presumably want to be having more children— educated working professionals— have some of the highest social standards for child rearing.
The Amish have the means because their means are not measured in normal dollar amounts. Most of what they have is traded and transacted outside of the dollar economy.
In fact, they may majority be of subsistence in which case the entire dollar value of all of their stuff is simply the land.
To me it seems rather obvious: you need both the will and the means to raise 3+ children.