Well, if oxygen is present the yeast don’t actually go into fermentation. Fermentation is what happens when the critters have sugars (pyruvate is really just half a glucose, so it can be thought of as a 3 carbon sugar) but don’t have a good enough electron acceptor (like oxygen) to break that 3 carbon sugar all the way down to CO2.
So, when all the oxygen is gone (and only once all the oxygen is gone) they can only break down the pyruvate part way to get some energy, and they end up with things like ethanol and acetate - that’s fermentation! This only starts happening at the end of the process. It’s called “fermentation” the whole time, but the yeast only perform alcoholic fermentation once they run out of oxygen. Your specific gravity is going to change the whole time, but will be more significantly effected at the end. At the beginning your “bricks” are going to change a lot more than your specific gravity. That means the yeast are eating the sugar, but not yet producing that much alcohol.
When they have oxygen, the pyruvate gets broken down into CO2 in the mitochondria - I would look more closely at the citric acid cycle, it should give you a better idea of how to make the yeast eat sugar better. That being said, you are right that if there is more oxygen then more things can survive. That can be avoided by proper sterilization.
If you’re looking to just mess with the existing pathways in yeast, you might be out of luck. They absolutely need Acetyl-CoA to survive and have evolved over millions of years to eat sugar pretty efficiently.
If you want to introduce a new pathway, you could look at cutting off the pathway to ethanol and driving it to acetate and then introducing a methanogen bacterial pathway. There’s no telling if that will work in fungi, and you’ll also end up converting your acetate to methanol or methane - which will make you go blind if you drink it.
That’s the trick with trying to get down to a single carbon without oxygen present - you get methanol. My suggestion would be to bubble in oxygen, which is going to increase the pressure so I don’t know how that will effect the forced carbonation, because that’s the only way you’re going to get more CO2 without producing things that might kill you.
Sorry for the rant.
-SG