I spent 35+ years in the aerospace industry as a machinist, mostly as a model maker. Drawing dimensions for aircraft in the vertical direction were virtually always referenced to a "Water Line". Note the term line was used here as mostly there was no specific plane on the part to use as reference as on the Flat/Table of a shotgun action. I very highly suspect using waterline as a reference point dates well back into the ship building industry. None of the "Air"craft I worked with however were ever destined to Sit in the Water submerged to a given line, yet the same term was used.
Water Table thus seems a perfectly satisfactory terminology & reference to me, Mr Webster (Or Wonko) notwithstanding.
I will note here that I have seen a few doubles which had neither flats nor table but the bottoms of the barrels were simply round & the bar of the action concaved to match.
