How to convert a PWM signal to analog
Various companies make fan controller ICs for 3-wire DC fans. I quickly found some of these ICs via an Internet search using the keywords "fan controller IC" and "3 wire fan controller".

For what it's worth, Mary Burke published an article titled "Why and How to Control Fan Speed for Cooling Electronic Equipment" on of Analog Devices's Analog Dialog website, and in the section titled "Fan Types" she states exactly what you've mentioned, that the TACH output on a 3-wire DC fan is only valid when power is applied to the fan.  According to Burke, a solution that is used by some of Analog's fan controller ICs is to momentarily turn OFF the PWM signal, and then momentarily apply continuous DC power to the fan to obtain a complete TACH pulse, and then to resume the PWM signal, adjusting the PWM duty cycle as needed based upon the measured TACH pulse data. In my opinion, this strategy should be doable with a suitable microcontroller and a few lines of code.