4-bit bus address selection via analog input pin: Monte Carlo simulation shows overlapping address values
According to your simulations, your addressing scheme works fine as long as only uncertainties in resistor values are considered. It's the uncertainty on the voltage that makes it fail.

My advice is to cancel out the fluctuations on VCC by using it as a reference to the ADC. You can do so by programming the REFS bits in the ADMUX register, as explained in the datasheet:



Once you switch to VCC as a reference voltage for ADC, you will not be measuring voltage anymore, but a ratio between resistor values, and those are precise to 1%. No changes are required in the schematic (though you may want to increase the value of R7 to get your measurements in the middle of ADC's conversion range), only the firmware of Attiny has to be updated.

If you're still willing to rework the sensor board, you can replace your schematic by an R-2R ladder as Cano64 suggested:







simulate this circuit &ndash; Schematic created using CircuitLab

This will optimize the resolution by making all steps in the ladder equal. 1% resistors are precise enough to build monotonic ladders of up to 5 bits.