I found that the 1N34A can be had from Scott's Hard to Find Electronic Parts which specializes in items for AM radio construction. The 1N34A is a full upgrade over the 1N34 and completely replaces it.
According to Scott, there is no substitute for the 1N34A due to its uniquely low forward voltage of 0.1 volt. Quoting that site:
Crystal Radio Receivers depend on the 1N34A Germanium Diodes rated
Forward Voltage Drop ( The amount of voltage before is starts to
conduct ) of .3 volts. Silicon diodes are rated around .7 volts.
However the voltage for the 1N34A Diode is measured with a current
around 10ma. As the current increases so does the Voltage Drop and
vise versa . However the 1N34A Germanium Diode actually starts to
conduct at very low voltages. The 1N34A will start to conduct around
.1 volt. So in a Crystal Radio Receiver you need only to produce
around .1 volt from your Crystal Radio Set to begin to hear a station.
That is the reason the 1N34A Diode is so popular with Crystal Radio
Germanium diodes are no longer made in the United States, possibly due to hysterical EPA rules about the use of lead as semiconductor dopants.