I believe I found the answer to my original question. You would need a well calibrated specific gravity hydrometers to gauge spirits by weight, if over 600mg of solids.
"However, in the case of spirits which contain solids in excess of 600 milligrams per 100 milliliters, the quantity in proof gallons shall be determined by first ascertaining the wine gallons per pound of the spirits and multiplying the wine gallons per pound by the weight, in pounds, of the spirits being gauged and by the true proof (determined as prescribed in §30.31) and dividing the result by 100. The wine gallons per pound of spirits containing solids in excess of 600 milligrams per 100 milliliters shall be ascertained by:
(a) Use of a precision hydrometer and thermometer, in accordance with the provisions of §30.23, to determine the apparent proof of the spirits (if specific gravity at the temperature of the spirits is not more than 1.0) and reference to Table 4 for the wine gallons per pound, or
(b) Use of a specific gravity hydrometer, in accordance with the provisions of §30.25, to determine the specific gravity of the spirits (if the specific gravity at the temperature of the spirits is more than 1.0) and dividing that specific gravity (corrected to 60 degrees Fahrenheit) into the factor 0.120074 (the wine gallons per pound for water at 60 degrees Fahrenheit). When withdrawing a portion of the contents of a weighing tank, the difference between the quantity (ascertained by proofing and weighing) in the tank immediately before the removal of the spirits and the quantity (ascertained by proofing and weighing) in the tank immediately after the removal of the spirits shall be the quantity considered to be withdrawn"