Sample and hold hold time

I am trying to figure out if the simple s&h circuit can hold its charge at a usable level long enough to update 32 units with only one dac.

Returning to the prophet 5 service manual, they indicate that their cycle time is 8ms, that they update 41 channels and that each channel update takes 20us for the DAC to settle and then 30-40us for the s&h to setle as well.

I made a little POC cirucit that held a mux output high for 25us then switched it off for 1ms. I could not see any drooping on the s&h (surprisingly it droops upwards towards 15V when nothing is connected to the input), but this is of course no proof as I am aiming for a very high output resolution - the Prophet 5 has a 7 bit dac whereas I will use a 14 bit one. Still, I will hopefully be able to update all 32 channels in around 0.8ms, which is 1/10th of the time it takes for the prophet 5, so it might not be impossible after all.

Top line is s&h output. Some noise is visible while the s&h is acquiring its value (when the bottom line is low), this may just be because I used an opamp 2.5V output as "DAC out".

I will try building a dual 16 channel s&h and see how that works out.