I'm now getting very repeatable waveforms using the photodiode and my analyzer is even able to consistently read the rs232 data! The problem now is that either the meter or the analyzer has bad timing: I said before that every "packet" in the 8 "packet" burst is identical, though now that seems not the case. There are very slight variations between the packets in a single burst: one or two rs232 characters may be different (FF vs F8) or a character is missing. I have two theories: either the meter takes readings much faster than it displays them and always send the current actual value, which due to PS noise, etc, causes the reading to fluctuate slightly, or the photodiode is not set up correctly to catch such brief pulses (the meter transmits at ~18000 baud). Until I can somehow get the data to be more consistent, there's too much variation to turn the data into a reading.
I had the idea today to use an op amp and voltage divider as a crude comparator to try and measure the IR led voltage directly to know for certain what a good transmission should look like. I think after probing the led directly, I'll keep the op amp to buffer the photodiode signal, as before it was going straight into the analyzer.