Variable Input Voltage Power Measurement
I think that by sampling the signal and integrating by SW you can achieve the results you want. Here comes the questions: What ADC resolution and what sampling rate. What quality of filter will you provide to concentrate on your required BW. Audio filters can be complicated because of their very narrow BW. The waveform type (with, without DC, etc.) is no issue for an integrating algorithm. It is only and issue for the analog front-end that has to condition the signal to the ADC range. Another limitations I see are the achievable accuracy, how to calibrate your HW/SW, and how to adapt the instrument to the range you specified, be it via mechanical/electronic attenuators and with or without auto-ranging.

Each option you want to add will be another complication of the SW. So, where to draw the line to keep it simple? Not easy to say.