What's your circuit?
Ill try over a few nights. This one I used a 386 chip op amp , the slight hum in the video is from wall wart ps which can be eliminated with a 9 volt battery but it rips through them. You can get decent selectivity by adding a trap or tuning the antenna coil and it also allows a longer antenna without overloading.
. The sensitivity is limited by the diode , not all are the same.
Circuit is just typical basic diode and with 250 uH coil and 365 uuf air variable condenser.
Not all diodes are created equal as you noticed. Had some old (50+ yrs) germanium
type, probably 1N34, here and picked the hottest of the bunch to use in the set.
Supposedly the old stock stuff is hotter than new ones... idk

The key is an antenna tuning unit inductively coupled to the tuning coil in the set.
The antenna coil is tuned by a couple of 365 uuf condensers in a switchable
series-parallel arrangement. The trick is getting the proper spacing when coupling
the tuner to the set. The closer the better for sensitivity but too close and selectivity
becomes bad to the point where stations are heard randomly all over the dial (no linear
"tracking" so to speak).
Have found that spider web wound coils seem to perform better than the usual
cylinder wound coils.
btw, you may want to try running the op amp on 12 volts (say a couple of 6 volt
lantern batteries in series or a sealed 12 volt VRLA battery, the VRLA could be recharged if
you have the proper means to do so), should run a looong time.