For the PCM56P-K You will see in the right bottom corner of IC housing big K,
without it, it is just PCM56P
They have simply measure the linearity of the DAC and the better ones become J or K on housing.
But it possible to have PCM56P with spec near J or K - because the demand for standar version was the biggest,
there is also PCM56P-L - low cost witch is worst.
Other Burr-Browns dac uses also small painted dot - one for J and two for K - it was withe or golden.
But this is not CD, there will be definnetly some improvement, but You will havemore improvment tweeking other parts of the circuit.
More important is power supply line - please replace the electrolitic capacitors for power supply lines of opamps with sanyo oscon - You can incerase the capacity, and remove the ceramic capacitors from the power supply decoupling line. Yhe same for headphone opamp, which i have not replace.
Replace also the capacitors around PCM56P power supply.
Remember that it is synergy between the power supply line behavior and the music.
Every opamp has his own signature - i have use here mix of OPA2604 and OPA2134
The opamp will burn-in during first 20-50hours and it will sound on the begining too agressive.
I have also change the bipolar electroitycs for Nichicon Muse ES - but the Elna BP is fine, i have measure it and it is still in spec after all this years.
Remember that only one DAC is used for 4 chanels - multiplexed by the YM3028 chip which can be the bigest problem of the signal path (here You can also replace the caps on power supply for Sanyo Oscon).
BTW.Sanyo Oscon is now Panasonic Oscon since few years, it is polymer capacitor with very good spec, and it simply sounds good but it needs some time to burn-in. But it is only for power suply decupling, not for the signal path.
You can also change the I/V converter of the PCM56P - You can use some extetnal opamp i/V converter on some fast opamp at least OPA604, but better will be some OPA627(sounds dry) or AD797 or some AD8xx - sorry i don't remember the numbers now - but the slew rate is important, and silver mica capacitors in the feedback loop does very good job. Other option is to try simple resitor i/V conversion - it is not so linear, but it is witout the (timing)errors of feedback loop , and sometimes it simply sounds better - You can read a lot on diyaudio.com formum about PCM56P I/V conversion. And check the .pdf for PCM56 - Analog Devices replecements also sounds a bit different AD1856.
Using higher bit dac will give You no improvement, and the signal level will be lower - with worse signal to noise ratio.