The question was asked if the single chassis Vinyl Song LCR phono might be compromised compared to the Cole LCR which has two boxes.

Not at all.
The Vinyl Song has also got 2 boxes! It's just that the transformers are placed inside an iron shielding box inside the Projekt box.

In fact the Vinyl Song has got 2 power transformers and is true dual mono from PS to output. Nothing is shared. This is done by using 2 special low flux power transformers instead of one big one in a remote location box.

There are other differences between the Cole LCR and the Vinyl Song LCR such as tube rectification etc. But they both got boxes.

And that's the way it is.