This is what I ended up getting, an SHT10-03.
I was not able to get it to work with the VantageVue. I'm not sure if there's an incompatibility or if I just damaged the small circuit board too much. The circuit board for the outside temperature and humidity also handles the wind speed, so I don't have wind speed readings anymore, either. I'm only getting rain data and wind direction from the outdoor sensor suite now.
I was able to get the SHT10-03 sensor to work directly with my Raspberry Pi, though, connecting it to the GPIO pins. I have the sensor wires run through the wall to the outside, to a covered patio. I wrote some scripts to combine the data from realtime.txt and the new temp/humidity sensor so I can display a simple dashboard on a monitor.
It will also display rain data, if it's been raining.
I am wondering if there is any way I can get cumulusmx to substitute the data from the new sensor for the missing data from the VantageVue. I wrote a script to replace the values in realtime.txt and upload the modified file, but it's much more involved than that to get it to use the new values everywhere. I'm not expecting there is a way to do it, but I thought it would be worth asking.