Multiple Buttons on Single Analog Pin and Trigger Pin Arduino Uno
Use the analog comparator in the ATmega328P to trigger an interrupt once the input voltage rises enough to indicate a button press.

Connect the analog network to both the analog input and D6.

If your lowest analog voltage is not greater than 1.2V then apply a voltage greater than 0V but more than 40mV less than your lowest analog voltage to D7. If you have not connected the voltage then configure the comparator to use the internal bandgap reference (ACSR |= _BV(ACBG)).

Enable the comparator interrupt and capture on a rising edge (ACSR |= _BV(ACIE) | _BV(ACIS1) | _BV(ACIS0)).

Disable the digital input on D6 (AIN0), and on D7 (AIN1) if connected to a voltage reference (DIDR1 |= _BV(AIN0D), DIDR1 |= _BV(AIN1D)).

Write an ISR that does what you want on comparator trigger (ISR(ANALOG_COMP_vect) { ... }).

Now go back and read all that three more times until you understand it. As always, see the ATmega328P datasheet for details.