AFAIK RF noise from computer may easely affect SPDIF signal causing timing error (which, actually, is jitter). So signal does get through, but with transmittion errors. External word clock link would mainly resolve this problem, but it indeed very rare option. And the difference in jitter situation between hard disk playback and CDP is in design and build quality between $200 sound card and 10-20 times as expensive CD player. Meaning that if you find sound card of the comparable quality and use it in hard drive music server that made with the same level of perfection (separate power supplies, isolated digital circuitries, etc. - to eliminate electical jitter) as a good CDP, you probably will get better results then in that good CDP.
Another way would be to eliminate SPDIF interface at all: use firewire or ethernet protocols, which can transmit the timing data encapsulated with the actual audio data on a very high speed, 100% CRC checked and confirmed, i.e. lossless. Thus, transmit music data from your computer in your office to a high quality network music receiver on your rack, which would just reformat the data from firewire to SPDIF in a protected environment without fans, multiple boards, and other noise-generators.
Another way would be to eliminate SPDIF interface at all: use firewire or ethernet protocols, which can transmit the timing data encapsulated with the actual audio data on a very high speed, 100% CRC checked and confirmed, i.e. lossless. Thus, transmit music data from your computer in your office to a high quality network music receiver on your rack, which would just reformat the data from firewire to SPDIF in a protected environment without fans, multiple boards, and other noise-generators.