Simple test…
Put some clear water on a stir plate and watch it, you will see there are a lot of small bubbles coming off the end of the vortex cone. As long as oxygen is in the air above the vortex it is being added to the starter wort.
Once all the nutrients are used up, it is done and needs no more oxygen. That is when we might begin to get cardboard flavors. Best way to get the desired yeast growth is to insure more than enough nutrients are in the starter wort to begin with.
Seeing the bubbles does not guarantee they are going in or going out. Furthermore, it does not guarantee they are O2, CO2, Nitrogen, or something else entirely.
Visual tests for things like this just are not enough. You would have to measure the actual level of oxygen within the fluid. Then, you still have to account for how much oxygen is getting in or out. Someone suggested diffusion, but that only works across a permeable barrier. In this case we have a raised, solid barrier which may or may not be covered. Thus, if there is something heavier than oxygen within it, we are not going to see the oxygen diffuse into the vessel. Instead, it will sit on top.
Now, there is some theory to the idea that spinning the liquid will cause fluid air above to match its rotation and cause an exchange within the flask. However, this defeats the entire purpose of an Erlenmyer flask, which is to maintain the integrity of the ingredients within it - which an exchange of oxygen would disturb. Furthermore, while some amount of air may get stirred and exchange the bulk of it will reach a point of stasis - unless you create turbulence by stopping and starting the stir plate. Thus, I just do not see much exchange of gasses going on here.
I think the additional attenuation you are seeing - which is roughly 10% as opposed to 100% for standstill versus shaken - is more to do with the suspension of the yeast and nutrients than to do with any hypothetical exchange of gasses.
You want to test this, you need to put several batches side by side, from the same mother, and test them simultaneously:
1) straight from the mother, uncapped, let it sit; (control)
2) straight from the mother, capped, let it sit;
3) straight from the mother, stirred, uncapped, let it stir;
4) straight from the mother, stirred, capped, let it stir;
5) shaken to aerate, uncapped, let it sit;
6) shaken to aerate, capped, let it sit;
7) shaken to aerate, uncapped, shake periodically;
8) shaken to aerate, capped, shake periodically;
9) shaken to aerate, stirred, uncapped, let it stir;
10) shaken to aerate, stirred, capped, let it stir;
11) bubbled to aerate, stirred, uncapped, let it stir;
12) bubbled to aerate, stirred, capped, let it stir;
13) bubbled to aerate, stirred, keep bubbling, uncapped, let it stir;
14) bubbled to aerate, stirred, keep bubbling, capped, let it stir.
And you could probably do a few more variations from there. Keep them all at the same temperature, same lighting, same area. Then at 12 hours, 24 hours, 36 hours, 48 hours, 72 hours take a pipette and measure the amount of O2 within them and the amount of CO2 inside the neck of the bottle; also measure the level of yeast at those times by taking a long pipette to the bottom, drawing it, and placing it in a secondary vessel for measurement (fridge, let it settle, measure).
Alternatively, know enough biology, physics, and chemistry to calculate all of this without having to do the actual testing.
