Halving the sample rate in mixing settings helps
You are probably running in VGA mode normally. But when you switch to a gfx card mode, the Amiga output is switched back to PAL.
Now the Amiga audio chips can sample up to 56 kHz, but only when the video is in DblScan (VGA) mode. In PAL mode audio is limited to 28 kHz.
There should be a setting in Picasso96 to switch the native display to DblScan while the gfx card is used. I don't remember the name, though.
Alternatively, when using AHI you can use the command
addaudiomodes DBLSCAN
