Unfortunately AJ, you are missing the forest because of the trees.
I don't think so. Let me explain why.
You speak of the validity of alkalinity going negative and I know you know that a positive alkalinity does equate to a bicarbonate content (within a certain pH range).
If I were to add 1 mEq of lime or lye or potassium hydroxide to a liter of DI water that water would have an alkalinity of (approximately) 1 mVal (mEq/L) or 50 ppm as CaCO3 or a "bicarbonate content" (calculated by the formula home brewers use) of 61 mg/L when in fact it contains no bicarbonate (nor calcium carbonate for that matter) whatsoever. Similarly, if I add 1 mEq of a strong acid to 1 L of DI water it would have an alkalinity of - 1 mVal or -50 ppm as CaCO3 or a "bicarbonate content" of - 61 mg/L even though it contains no bicarbonate or calcium carbonate whatsoever. What we are interested in here is a proton deficit or surfeit and we have names for those, respectively alkalinity and acidity (though we can consider acidity to be a negative alkalinity) and units for clearly and unambiguously expressing them. These are the mEq/L and mval. When a sample is submitted to a laboratory for analysis the pH is measured and the sample then titrated to a reference pH (acidity and alkalinity must be specified relative to a reference pH) with acid (alkalinity measurement: sample pH > reference pH) or base (acidity measurement: sample pH < reference pH). The alkalinity or acidity is the number of mEq of acid or base required to reach the reference pH per liter of sample. What has been measured
is the proton deficit or surfeit wrt a particular pH and mEq/L (mVal) is the natural unit of alkalinity and acidity and these are the units used in water reports outside North America. In the US we use the proxy unit 'ppm as CaCO3' which is 50 times the alkalinity/acidity in mVal. This is done because if 100 mg of CaCO3 is dissolved in a liter of water
using CO2 as the acid and bring the pH to 7 then the hardness and alkalinity of the water will both be about 100 ppm as CaCO3. This practice has confused a lot of people trying to understand how this stuff really works because what we are really interested in, when it comes for example, to attempting to predict mash pH is
proton deficit or surfeit.
Therefore, while you are correct that there is never truly 'negative bicarbonate' content, there certainly is an allegory that acid content can be translated to a negative bicarbonate content (or alkalinity demand) for a water.
As indicated above, the 'proper' unit for alkalinity/acidity is the mVal. There are several other 'allegory' units abroad as well. The aforementioned 'ppm as CaCO3' which is 50 times the mEq/L expresses things in terms of the number of mg/L CaCO3 dissolved in a particular way. While use of this unit is to be deprecated for reasons alluded to above we are sort of stuck with it because in brewing we are ruled, in the US at least, by the MOAs of the ASBC and Standard Methods for the Examination of Water and Waste Water is incorporated into the MOAs by reference and those standards use ppm as CaCO3. In Germany °dH, in which the mEq/L are multiplied buy 2.804 are in common use and in France the °F in which the mEq/L are multiplied by 5. Martin seems to like to multiply by 61 and I'd like to propose the °AJ in which the mEq/L are multiplied by Euler's constant (0.57721).
Users of Bru'n Water will recognize that there is indeed a negative bicarbonate content that can be ascribed to brewing water and it is a valid way to describe the effect of acid addition.
If you are going to use one of the deprecated units you should, IMO, use the one that is accepted in the industry and not one you made up yourself. I also think you are obliged to point out that this number is not really expressive of bicarbonate content. If we say "alkalinity, ppm as CaCO3" the 'as' suggests that we are not really talking about CaCO3 content but are using this proxy to express proton deficit. Similarly if we say "alkalinity, °dH" or "alkalinity, °F" or even "alkalinity, °AJ" we know that we are talking alkalinity (proton deficit). But if we say "bicarbonate 77" that suggests that the bicarbonate content of the water is 77 mg/L. If you insist on using this unit you need to say "alkalinity, as bicarbonate".
I know it offends you, but its still workable and valid.
Given that you have perfectly good, unambiguous, exact units that do not depend on pH and are valid whatever the actual chemistry of the water why would you use anything else? A possible answer, though it still offends me, might be that 'ppm as CaCO3' is widely used in the US to express acidity and alkalinity and is accepted by ASBC and AWWA. But mg/L bicarbonate is not accepted in either of the industries (AFAIK - in fact I've never seen anyone express alkalinity/acidity 'as bicarbonate' before that I can recall) so why try to force it on home brewers? Is there some benefit to it that I'm missing?
I think those of us that have been dubbed experts should try to lead aspirants along the path of accepted practice. This does not mean being closed minded to new ideas but I'm afraid I just can't see any benefit to expressing alkalinity in units of mg/L of anything. "As calcium carbonate" or "as calcium oxide" isn't good either but at least there is precedent.