Unfortunately, the only solution I've found for the FT-60 has been to put a headset into an external speaker mic.
Also, the FT-60 has some nasty bias voltage (~3v!) on the audio output, which makes a loud thump in a headset when the radio unmutes. One solution is to make a short jumper cable with a 3.5mm stereo jack on one end and a mono plug on the other. In my case, driving a Sony 7506 headset, two .33?f dipped caps in parallel with the audio signal fit neatly in the stereo jack shell,?one lead to the tip and the other across both audio lines in the cable. They block the bias voltage, and also filter out a bit of low frequency noise.
The thumping is not as much of an issue with earbuds, as the smaller diaphragms in the earbuds don't jump around as violently as the larger ones in over-the-ear phones.
Rick
KK6WHJ