Re: "If there is DC on the output of C1, the cap on the input to the next stage will block it whether R3 exists or not . If the next stage does not have an input cap, any DC on the output of C1 will still appear on the input of the next stage whether R3 exists or not. What am I missing? Or is it there simply to bias the electrolytic?"
You are missing that when plugging or un-pluging your input connection from your Mic circuit; there will be a leakage voltage appearing on your Capacitor C1 which may well exceed your Soundcard maximum input as it is not conducted to ground by the Resistor R3.
When you connect with a charge or leakage present you are applying a voltage pulse which can also exceed your input in terms of it's conduction via it's input capacitor! PC Soundcard often runs on 5V DC and your circuit is approaching 30V DC.
Hope this now clears it up - might be explained better by others though!
As to your CCS, have you investigated the noise from the IC you are looking at?
You may well find for the low current you are seeking that a discrete CCS circuit is more suitable
Mik