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Kinda crazy but why not use some kind of pressure sensor to measure the weight of the tank?
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Strain guages mounted on the straps, or maybe just on the bottom of the tank. The tank bottom or support straps will deflect more with added gas. You will only measure weight, not volume. You will have to remove the gas cap to de-pressureize the tank before you measure. Naturally using gauges in all 4 legs of the bridge will help negate temperature effects.
Strain Gages, Accessories and Instrumentation