Problem programming Mini Pro via Arduino as ISP
After poking around for a bit more, it turns out my problem was the baud rate.  I could make it work by setting it to 19200, just a little slower.  Alternatively, you can modify the ArduinoISP sketch to enable higher baud rates.  I used this post to enable 115200 baud and I was able to successfully use avrdude at the higher rates.

Not sure how I missed this before, but it's an easy to solve at least.