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What numbers? The text provides no data that would allow us to "run the numbers.

Pretty lame.

The volume in Litre (L) in cubic metre (m3)is: 1000L/m3.
21 % of the atmosphere consists of O2 by volume. So, 1000 L of air consists of 0.21 x 1000 L = 210 L of O2.
1 mole of any gas at STP has a volume of 22.4 L. Therefore 210 L of O2 is 210L/22.4L/mole = 9.38 mole.
The mass of 9.38 mole of Oxygen is: 9.38 mole x 32 gram/mole = 300 gram or 0.3 kg.
According to NASA the average person needs 0.84 kg of O2 per day (day and night activity).

So for a room 12 ft wide x 12 ft long x 8 ft ceiling
3.6 m x 3.6 m x 2.4 m = 31.1m3
would last 1 person about 2.6 days, divide that by the total number if more than one. Does not include respiration by animals or other biological activity.

Now consider crossing the pacific ocean, from the article of the thread "Ether describes heavy seas (" . . . they were many times buried in the depths of the sea, because of the mountain waves which broke upon them" 6:6). 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)." Pacific storms would keep them bottled up for days - still having problems doing the math?

They are of necessity for a moon pool to function within a boat - do your research better.
You are mistaken.

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.

still having problems doing the math?

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?

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?