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I'm 100% sure the empirically determined value is correct. Does anyone have any idea what is wrong with the calculation above?
Any of the input parameter. My guess is the sensitivity of the sensor, post a link to the sensors datasheet. Another one might be the wiring, remember you're handling voltages in the µV range, so short unshielded signal paths may result in wrong readings.
That approach won't work well with the ADS1115, because it is an absolute ADC, with its own voltage reference.
To make accurate measurements from a ratiometric sensor like a bridge, you need to use the ADS1115 to measure the sensor supply voltage as well and form the ratio(s) in code.
Use the 6V input range. To check the scaling measure each side of the individual sensor outputs with your multimeter, and with the ADC to make sure they agree. Note that the single ended resolution is 15 bits.