I'm far from an expert, but since no else is responding, I'll throw in my thoughts.
If I understand right, the acid phase of an A/B extraction serves 2 purposes. The first is to break down the plant material. I believe that this is why heat is important during this stage. The second is that it converts all of the DMT to a salt. The DMT should exist as a salt in the plant (I recall reading a post a while ago that said it's the tannate salt, but I'm not certain of that), so this is not all that important.
So, the question can really be broken down into two parts: how much acid solution is required to break down the bark, and how much is required to convert the DMT to the appropriate salt and dissolve it?
I expect that the answer to the first is however much it takes to cover the bark, so long as the pH is high enough, enough heat is used, and the cooks are long enough. The answer to the second obviously depends on a few things. The amount of acid needed to convert the DMT to salt form will vary with how much DMT is in the bark, but the amount of water can be adjusted to keep the total volume constant, and excess acid should be used anyways so that it will not matter, so that is not particularly important for the question. The volume of acid/water needed to dissolve the DMT salt will vary with which acid is used and, thus, which salt is obtained. This is because different salts have different solubilities, just as the freebase has a different solubility from the salts. However, because they are polar, the salts tend to be quite water soluble. If I have time, I'll look and see if I can find some exact numbers, but I expect that the volume it takes to cover the bark is more than sufficient to dissolve all of the DMT. If that is the case, then the answer to your question is simply "enough to cover the bark." Otherwise, the answer will be "enough to dissolve the DMT," which will vary with chosen acid and the DMT content of the bark. Assuming, of course, that I have not made any mistakes, overlooked anything, etc. The quote you posted seems to indicate the former. The linked post says:
Psilosopher? said:
Therefore, 500 mL of this acid can theoretically dissolve 10g of DMT.
Dividing by 5, we get that 100 mL would dissolve 2 g of DMT, about what one would expect from 100 g of MHRB. So, if one were using hydrochloric acid of the specified concentration, 150 mL should be more than enough. In my limited experience, it takes more than this to cover the bark, although I have only used shredded.
So, from all of this, I would tentatively answer that the minimum amount of water is enough to cover the bark, multiplied by however many cooks you do, since you will need to cover it each time. I will again say, though, that I am far from an expert. My knowledge of the relevant chemistry is weak, and my practical experience all but nonexistant. I would also add that I do not understand the idea behind multiple acid cooks. I realize that they are supposed to increase yield, but I do not know how. The author of the post you linked says elsewhere in that thread that he only does one cook and has good yields, and cyb's teks only use one cook, so I am very confused on the theory behind multiple cooks. So, obviously, there are some gaps in my knowledge. Take this post with many grains of salt. Hope it helps a little bit at least.
I look forward to the results of your experimentation. I would also suggest trying a single acid cook that takes x times the length of your normal acid cooks, where x is however many cooks you end up doing, then comparing the yields. This would give some information on whether it is the quantity of acid cooks done and/or volume of water used or the length of time cooking that is important. This could also be tested by doing (1/2)x cooks for twice as long or similar. Similarly, it would be good, as you seem to discuss in your last post, to test fewer cooks with more water to see if it is, in fact, the quantity of water that causes multiple cooks to increase yield, or if there is something else causing that.