dhenry:
it would be 31*1ms.1ms is for the shortest duration (a '1' at bit 0 if you will).
A short PWM_Bit will improve ripple, and response time, but it would tie up the mcu more.
I think 50us is probably the bare minimum you can go and I would actually go with a 1ms as that is more than sufficient for your stated response time of 1s.
I tested 50 us and it worked for 12 channels. This means a PWM frequency of 1/31*50 us = 645 Hz.
Tested it with a R of 1 kOhm and a C of 47 uF -> this gives a ripple of 0.04 V p-p
Tested it with a R of 1 kOhm and a C of 4.7 uF -> this gives a ripple of 0.4 V p-p