I recorded most of my vinyl with a normal Amp. All CD-4 were noisy, destroyed. Later I got the idea what I recorded: the carrier.
My Compi has only 2 ch input, so I can't record 4ch as with my tape (now the heads are down) and externe like Tascam etc. were not available at that time.
Recording the native CD-4 is very easy: solder a wire (2 of course) after the RIAA pre amp, before the low pass filter. A very stable signal, good to edit.
Luckly my old XP compi could record up to 192/24. Win7 and later is blocking this. Now it's only possible with extern analog to USB recorders like Tascam etc.
You can also do a needle drop, as most do it, record the tiny signal that comes from the magnet system. I stopt that when I heard neighbors telefone in the recording.
For play back you can use the same wire, but you have to cut the connections to the RIAA pre amp. A little switch will re-connect it for recording (so you have now 4 wires connected at the switch.
Play back from compi, DVD or better a media player. If it don't work - disconnect the HDMI, the handshake with the TV will limit the players output to 20kHz or so (use RGB).
(CD-4 carrier is a frequency stable 30kHz signal, you will see it in Audacity)