Just tried AsimCDFS 3.10 but when I enable "Amiga Audio" in its CD player program, it can't transfer music to Amiga well 
What that option does is transfer the CD audio over the data cable (SCSI) rather than the analog outputs on the drive. There's some CPU-intensive data conversion required, which is why you're getting choppy output and a slow system.
If you can capture the analog audio directly from the CD drive then that option won't be necessary. And you'll be able to get CD audio from applications other than AsimTunes as well (i.e., games). I think
this thing from Amigakit will do the trick and mix the Amiga audio and CD audio into one set of outputs. Amigakit sells another cable that just gives you RCA outputs from the CD drive so you can connect CD audio externally to an existing mixer.
If you've got a lot of audio sources, something like
this Rolls mixer might be a good choice. I use one to merge Paula, a Sunrize 516, and a OneStopMusicShop. There's also a cheaper
unpowered version that might work. You'll need a lot of Y-cables, though
