I did a little more experimentation. A 1N4148 also worked, but not as well. A RK44 did not work at all.
Sticking to the 1N34A, I found that by cooling the RF output transistors by blowing cold air over them, the measured voltage increased from 2.09v to 2.68v! Assuming the measured DC voltage is proportional to RF RMS voltage, that is an increase of power by a factor of 1.6! I repeated that several times to make sure it wasn't just measurement error, and the results were the same: the output would increase after cooling and slowly dropped back down as the transistors warmed up.
Next, I connected a bright red LED to the diode and I was just barely able to make it glow from the RF power. Finally, I connected the diode to a pair of headphones and made a simple crystal radio for the 2.4GHz band. 802.11 sounds like a helicopter or machine gun from the periodic SSID broadcasts, with bursts of buzzing from data packets.