But in the new incarnation, I don't need to do that. I only need five pins: two for the pseudo-I2C, one for receiving the random bits, and two analog/digital converters so that the average speed and average interval can be tuned with pots.
It just so happens that the 16F628A doesn't have A/D on board. But the tiny 8-pin 12F675 does -- a three-channel one, at that. And it has six pins available for I/O, which means I could use that one in the 'master module'.
It takes quite a bit of time to check all these details (I'm getting better at reading datasheets, though), but I find I enjoy the process of implementing whatever specifications I have thought up with the cheapest/tiniest materials. I have some 12F675's lying around too, so I could start experimenting with the A/D module too.