Oliver, I think you summed it up very well, much the same as my personal experience having bitted the Pi/DAC/Caiman SEG DAC bullet. I presume you have borrowed and not purchased at this stage.
If you decide to go ahead then you had 2 choices really, the route I took and then if your CDP has S/PDIP out you can feed the Caiman SEG DAC or similar external DAC, this is very likely to improve the CD replay(but I am not sure that you have one). Alternatively by a RPi with a higher end DAC card, like ALLO – KATANA DAC or TERRATECHNOS – TERRA-BERRYDAC 2+. If you want to spend a bit less but still get really good SQ I understand that this is a good option RPi with ALLO – KALI I2S RECLOCKER and compatible DAC (have a read
https://volumio.org/product/allo-kali-i2s-reclocker/)).
Enjoy sofa sound surfing.