The Point: ASC Not Practically Useful
There is no ambiguity in my mind here, though you seem to be getting my point. The claims of Marks is entirely about what can be computed from data. He makes the claim that ASC is good way of empirically measuring CSI. That is the whole purpose of the study. In this context we do not know the true P, but can only guess it. If the result is dependent on choice of P, then his entire claim is false. Essentially, as you put it:
Which is to say that ASC is not useful in a practical setting, contra his claims. That is precise challenge I am making. If ASC is not practically useful, we still have no way of measuring CSI (as Marks admits in the paper). This leaves CSI as very poorly defined concept without any way of engaging real data till his problem is solved. I know there are other attempts to solve this problem, but they all have analogous defeaters.
Valid Choice of P
Your criteria for valid estimated P is interesting.
We can prove criterial is only satisfied if and only if \forall X, P_{ext}(X) = P_{true}(X). Remember, that P is normalized, so that the sum across all X equals 1. So too much density for one outcome, has to be compensated for with too little density at some other outcome, which would violate your inequality. Therefore, by your criteria, the estimated P is only valid if and only if it exactly equals the true P. I certainly agree.
The criteria you’ve put forward makes my point. The inequality ASC < CSI only applies if you know exactly what the true P is, but we do not know the true P for any biological sequence. ASC is, therefore, practically useless. Remember, the only valid P is the true P, so we have no way of constructing a valid ASC.
That was not my claim at first. Though it appears to be true. If finding a valid estimated P is equivalent to finding the true P. That is impossible. Finding the true P is equivalent to finding the ideal compression, which we know is uncomputable. There is a simple algorithm for transforming the true P into the ideal compression. So if we can determine the true P, then compressibility is computable, However, we already know that leads to contradiction: compressibility is not computable. Ergo, determining the true P of, for example, DNA is provably impossible.
What is at Stake
It seems we are tracking very closely with the logic of the paper. You’d have to show where you deviated from the logic of the paper. Or perhaps, where they went wrong. This is, after all, your idea that they have developed.
That does disprove the claim that ASC is a valid way of measuring CSI. This the whole point of the Marks paper on ASC, that he has found a practical way of measuring ASC, and therefore a practical way of detecting intelligence. If this turns out to be false, the entire point of the paper is overturned.
The Interesting Claim
That was not my earlier claim.
Rather, my earlier claim is that I can construct a sensible P which will almost always yield an ASC of zero (if not always). I can both empirically demonstrate this and prove it too. If that is true, one of two things is also true:

Either ASC is not useful in a practical setting for measuring CSI, because it more determined by our choice of P than any signal in the data.

Or CSI is precisely zero for all objects encodable as strings (i.e. everything), and we therefore find no evidence for intelligent design using CSI.
We will go further, but will be interesting to see which path you will take on this. Either ASC is useless practically for measuring CSI, leaving CSI as a signature of design but unmeasurable; or ASC is correct and useful practically, but it demonstrates that ASC does not empirically find CSI in anything. I’m not honestly sure which one is a better conclusion for ID. Both are going to be difficult to work through.