Perhaps you should get a 3 volt mini. And an op amp that works at 3 volts as well.
I don't see how that would avoid the OP's problem, Chris. There would still be a short circuit as the plug is inserted into the TRS socket. The OP tried to limit the short circuit current with a resistor, but that won't provide the Pro Mini with a stable supply, even if it is a 3.3V version.
Why won't the supply be stable with a resistor in series?
Because the current drawn by the circuit won't be constant. It will vary from moment to moment depending on what the Pro Mini is doing. And because of Ohm's law, the voltage drop across the resistor will also vary.
You are right Paul. I had interpreted the problem as the voltage dropping from the resistive fix, and the op amp not working properly. I hadn't really considered the mini's current requirement, which is the real problem. Fixing the power glitch is surely the way to go.
Maybe you should indeed go to 3.3V for your Pro Mini (and run it at 8 MHz), but then using a linear regulator such as the AMS1117-3.3 which has short circuit protection built in (the current is limited to 1.1-1.2A).