A first improvement would be to lower the current by lowering the voltage with a voltage divider (potentiometer). The sensor will still work if the Arduino only reads e.g. 200 instead of 1023. If you used an operational amplifier, this could go even further.
The 2nd step would be to just read the level every e.g. 2 seconds for a very short time. So activate the sensor by using a digital pin as the voltage source and turn it to an output and set it to HIGH. Then read the analog value and turn the sensor off by setting the pin to input (internal pullups must be off).