The best sounding I2S wiring

Well it's just your assumptions.
I'd like to address those - point them out please. I've noticed you made the assumption that the designers of your DAC knew enough to avoid ground noise issues.

The question is why an analogue contamination (if this is the case) could occur when all I did was just use 3 different methods of connecting converter to DAC? And the analogue section is isolated from the digital one by ADUM.

The ADuM isolators have relatively low capacitance in-out (I think around 2pF) but there is likely a route between groundplanes which has higher capacitance than that in your DAC. For example if the analog and digital supplies are both fed by separate toroidal trafos (quite a common occurrence) there will be much more coupling between them via trafo parasitics than through the ADuM.
 
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In my case the sound source is a sound card in a PC with AES/EBU output going to the SPDIF - I2S converter and then to DAC. Could it be that some noise was coming out of the PC with the signal? On the other hand when I experimented with optical connection between the sound card and converter I did not hear any advantage of optical connection over coaxial connection.
It's often said that optical SPDIF is prone to more jitter than coax so any advantage of the galvanic isolation may be negated.

PC's are notoriously noisy for audio so it wouldn't surprise me if this is the source of the noise.
 
It's often said that optical SPDIF is prone to more jitter than coax so any advantage of the galvanic isolation may be negated.
Of course optical connection is very jittery but isn't synchronous reclocking within the DAC supposed to rectify that?
And one more thing. Let;s forget about the optical connection because I made these experiments at coaxial connection between PC and converter.
 
None of the 3 connections in OP have proper terminations so signal integrity may be an issue. Scope should help to find out if there are severe over/undershoots or reflections which may cause data errors that are perceived as noise. Another possible issue may be propagation delays which may cause data errors in reclocking (e.g. due to metastability if flip-flops are used).
 
How does the 33MHz signal from the Golledge oscillator reach your soundcard?
The clock goes to a flip flop and at the same time it is divided by 2 and then goes to converter where it is converted into SPDIF signal by DIT4192 and then it gets sent to the souncard as SPDIF signal and the card is synchronised to that incoming SPDIF signal. That's how it's done.
 
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There's plenty of 'slop' in that locking arrangement so whilst I take back my 'asynchronous' reclocking remarks, there's still plenty of possibility for metastabilty as there's nothing ensuring the ABT574's set-up and hold times will be met.

Is the Golledge osc actually running at an audio multiple frequency like 33.8688MHz?