My concern about the amount of foam is driven by the assumption that it is representative of the amount of oxygen dissolved in the wort. Assuming that the dissolved oxygen is the real goal in shaking, maybe my assumption about foam representing that quantity is flawed. In the end we just want to dissolve as much oxygen as the 3 quarts of air in the jug can provide, yes?
Opinions vary... here is mine, $0.00
My theory is the shaking distributes the yeast in the wort very well and that is pretty much the limit of its value. I do not think the foam is introducing any more oxygen to the wort than was already in it before you started shaking. I say this having not even tried an SNS starter yet, but I can see why people would prefer this method and I have no doubt that it works just as well as any other.
Pure Oxygen dissolves into a liquid at a pretty good clip. Pretty much about as fast as you can provide surface area, it's absorbed to saturation. I'm not sure if the mechanics of it are entirely the same when we are talking about oxygen in the atmosphere, but given the fact that you can pour your perfectly good beer onto a plate and take a sip within 2 seconds and it's already oxidized and horrible, I'd say it still happens pretty fast.
If you want to know how much oxygen is indeed being absorbed by the wort, put it in your container and seal it with a lid that has an access hole for a blow off tube. Obviously a tight fitting one with no leaks. Add the tube and run the other end into a bucket of starsan. Now shake to your heart's content. The amount of oxygen dissolved into the liquid is precisely the amount of liquid pulled up the blow off tube into the wort. If you shake the first time and you are not scrambling to get that blow off tube out of the bucket before the starsan gets into your wort, then that should be telling you there isn't much oxygen being introduced by the foam. My guess is it's already in there from the time you allowed it to cool.