Open auction, with price going as high as it wants, right down to zero.
Special categories (e.g. multiple co-morbidities, medical workers) cut to the front, and pay market rate.
Let businesses foot much of the bill. If I need to pay $1000 to reopen my factory, it might be a good investment. Free market will allocate resources.
For extra credit: https://www.tpr.org/business/2020-12-17/tyson-foods-fires-7-...
But, offering the middle/upper income class a $1000 chance to jump ahead could generate just as much money with a much larger population getting protection.
Second, are manufacturers interested in filling that 6 billion gap? They can already afford to build the infrastructure and make more vaccines, but it doesn’t do any good if there is nobody to buy them and no way to get them to patients.