This sounds like a very cool idea. Agree, tempo subdivisions and multiple alternative waveforms would be great (sample & hold and/or random would be cool, too).
I don't recall ever hearing of a tap-tempo pedal that could do this, and it surely would be a challenge, but... How about a tap-pattern mode? IOW, maybe a rotary switch could be used to set the number of taps for the chip to accept as a pattern (ie- 3, 4, 5, 6, 7, 8 ). Now, suppose you set it to 5. Then, corresponding to the last five taps that you make, whatever timing differences you tapped in would be repeated. For example... 1 - - - 2 - - - 3 - 4 - 5. Actually, I guess if you set it to 5 you would probably have to tap 6 times in order to get the timing for going back to step 1 from step 5 in the pattern. Anyway... just a wacky thought.
What is the sweep waveform? Similar to ramp or saw?
What is the noise waveform... white, pink, etc.? Is there really any tempo associated with noise?
Any constraints on the duration of each tap or the number of taps needed to set or change the tempo? The more idiot-proof the better.

~ Charlie