G3EJS has used a PIC processor to sequence the mute of the RX and change to TX. The PIC responds to the PTT going low by muting the audio amp, and 100ms later, passing the PTT low state to the raduino. When the PTT is released, it stops the PTT to the raduino, then 100ms later un-mutes the AF amp. He then made a breadboard version, which resulted in a silent transition.
G3EJS then made some boards and finally integrated a number of mods onto a single circuit board. Check out his pop mod circuit below: