Can’t speak for your system but I have a CA 851C and on this player balance cables do sound better if your preamp is a balance circuit which your ML is. You should notice a lower noise floor which is going to clean everything up, less grunge, more open and relaxed sound.
As far as cables go, you mentioned Canare which I am very familiar with. I would suggest pick up or build a set of their mic cable with some Neutrik XLR plugs. I use this cable, several, to mic my drum kit and have used it in my HiFi and it can hold its own. My opinion on the Canare is an open relaxed presentation, not the most revealing but pleasing. What it will do, is show you have dropped the noise floor with the balance output on your 840C.
I’m sure your Mogami is fine and my guess is the Canare SC will be a parallel move. As far as PC’s go, use a heavy HC, high current power cord on your ML and on your 840 use a well shielded PC.
Your ML is probably a hungry pig and needs good power from the wall, so get dedicated circuits with quality receptacles/outlets or you’re starving it. You’ll be more amazed what dedicated circuits will do over trying balanced cables, and power cables will not make as much of a difference if you’re feeding your amp with a No.14 romex circuit shared with numerous other devices. You want No. 12 if not 10 for your amp to deliver its full potential. Your amp will sound lean and bright if you don’t have the juice to drive it. If you don’t have heavy dedicated circuits, do that first or you’re wasting your time and money.