OP, you said that the Freya doesn’t give “a true version”.
it wasn’t designed with home theater bypass features. I suspect you are going to have to spend a whole lot more than the Freya’s price tag to get something that gives a truer version. I’m not sure anything exists in the boutique brands that has some kind of theater bypass.
You mentioned having other systems, I’m in your boat with a total of four systems these days, although one is just for swapping in gear and comparing. Perhaps it’s just best to not do 2 channel in the Freya set up?
Or, in one set up, I inserted a Schiit Sys between the AVR and the 2 channel mains amp. I connected the CD player on one input, and the AVR signal on the other input, and the amp on the outputs. This allows me to toggle between the CD spinner and the AVR, for a quick and dirty 2 channel option. The Sys has a volume control. For $50, maybe it’s worth a shot?