but I was wondering whether there exists some sort of IC that would drive the sensor and convert its pulse output into an analog voltage output. So that the Arduino wouldn't have to switch pin mode and measure pulse width, but it would just read a voltage analog input continuously.
There are other "minimal" processors that could do the job too..
Don't know much about the ATTiny - but could you instead output PWM and use a cap hanging off the pin to "output" an analog voltage level...? Main question would be if there are enough pins/resources to do that...