How to handle large number of analog inputs and outputs
If I had to do it this way I would consider something like the Dallas DS2450 1-Wire Quad A/D Converter. These feature a very simple data-bus and you can daisy chain more than enough for your synth application.

The big problem - and it could render the system useless - is that it will be very difficult to edit a patch. If you recall a patch then your pots are no longer in control and don't show you the settings. (The pointer positions won't bear any relationship to the settings.) To change a patch you would have to activate the knobs again and re-enter the patch.

One small possibility is that you reload a patch and then monitor the pots. If you sense that one is being adjusted you switch to live mode for that pot. This would require that you create a deadband so that random ADC noise does not falsely trigger reversion to the knob. It would be a little weird: if the patch is at 80% and the pot at 20% with a 5% deadband then adjusting to > 25% would make the pot take over and that parameter would jump from 80 to 25%. You would then adjust back to 80% by ear and start the adjustment from there.

Interface modules are available for the Dallas 1-wire system. I recommend these as they remove the critical timing requirements from the CPU to an external device.