The problem is not the math but the data, or rather the lack of data:
1. You do not know the volume of the vessels.
2. You do not know the types and numbers of animals on board.
3. You do not know how long the air hole had to be stoppered.
4. You do not know how long it took to replenish the air when the hole was unstopped.
So these boats were crashing around under water, occasionally flipping upside down (thus the need for a hole in the bottom which could be opened as an air hole when the boat flopped over)."
How often did they flip upside down?
Google 'moon pools' Logo. You will find that even your best scenario would require the sides of the moon pool to be quite deep ( greater than the draft of the ship by a margin of safety) in order not to sink the boat.
At least we agree that a moon pool does not require an airlock; that is progress.
We also agree that the sides of an airlock-free moon pool (assuming the barges had moon pools) would have to be higher than the draft of the vessel.
So tell me, what was the draft of a barge?
Actually my approach was conservative - man at rest.
1. You do not know the volume of the vessels.
To be sure they had to be big to handle the flocks, people and supplies. One sheep will eat over 1000 lbs of food in a year, let alone the amount of water needed.
2. You do not know the types and numbers of animals on board.
Once again, a lame assertion. Are you making excuses for the bom? Flocks of sheep, live fish, birds as well as other beasts of burden (camels and donkeys). Plus the supplies necessary to get them through one year.
3. You do not know how long the air hole had to be stoppered.
As noted, even short periods during storms will result in rapid depletion of the oxygen - "many times buried in the depths of the sea" (6:6) and "mountain waves" (2:24) Oceanic storms for a drifting craft will last for days - add the stress of increased oxygen consumption of people and animals during these storms (I'm sure being 'buried in the depths of the sea' will get anyones heart racing). And those are the basics. I've noted other biological consumption of oxygen which you apparently fail to comprehend. One of these is aerobic and anaerobic bacteria processing the stored food for the livestock and their waste. Ever been to a stockyard? Take a good wiff the next time. Anaerobic activity creates an even greater hazard - hydrogen sulphide, a heavy gas that is difficult to get out of a confined area without active ventlation - the topic of your next point
4. You do not know how long it took to replenish the air when the hole was unstopped.
To replenish such a vessel, it would require an extremely large hole - and these holes are an after thought in the mormon god's mind from the bom narrative. A hole will only be slightly better than diffusion for oxygen exchange and will do nothing for heavier gasses like H2S and CO2. Don't believe me - next time you go down the street, take a close look a the workers in confined areas beneath manholes. What do they all have? They have a BIG fan and ducting forcing fresh air into that space. A passive 'hole' in the top of an otherwise air tight ship after an expended period will not 'replenish' the air.
How often did they flip upside down?
Apparently often enough for the mormon god to retrofit these barges with two 'openings'
At least we agree that a moon pool does not require an airlock; that is progress. We also agree that the sides of an airlock-free moon pool (assuming the barges had moon pools) would have to be higher than the draft of the vessel. So tell me, what was the draft of a barge?
When one considers the tons of food, supplies, animals and people each would need, common sense would indicate that it would be riding low in the water. If it rode higher in the water it would be prone to tipping over easily (higher center of gravity) But we already see that the mormon god retrofit instructions do not include instruction to add 'sides' to the moon pool. Secondly, absent an airlock mechanism of some kind, being submerged as claimed in the bom, water would come gushing in rather easily (along with interior air exiting).
So build/design us an airtight barge that can carry a herd of sheep, all their provisions for a year (food and water), people to care for the sheep (with food and water for themselves)capable of handling Pacific storms (being sealed for several days), flipped over a couple of times each storm and perhaps you may have a reasonable arguement.