I'm very happy to report that it is working flawlessly!
I got an accurate scope reading by connecting the probe to my signal wire (the tip of the TRS connector) and grounding it to the sleeve while the recorder and remote were connected. A simple Arduino code using multiple digitalWrite's and delayMicrosecond's allowed me to recreate the signal exactly, and a voltage divider got it down to 2.9 volts which has so far been perfectly reliable. Thanks for your help MorganS! I have to return my borrowed oscilloscope tomorrow and I'm so glad you were able to help me find the best way to use it before then.