I have a loud "ptt-click" too in my BITX40.
I read some articles about the LM386 where it was mentioned that grounding pin 7 can be used to temporarily mute the audio.
Perhaps this feature could be used to cure the "ptt click", just by switching pin 7 to ground during transmit. Has anyone already tried this?
73, Allard
Allard PE1NWL