How best to arrange cables in this room...

don't even concern yourself with unequal length cables its a none issue at these lengths. 

@carlsbad2

+1

…”Equal length cables are always recommended, I’ve played with un-equal length and never been able to hear the difference. ”

I have to agree. While I did not do this when I was tremendously experienced with high end audio. In the end, I always have purchased equal length cables. If you are an audiophile, then go for equal lengths. I doubt I could stand realizing I had vastly different lengths. An audiophile system is the result of having no small compromises, they add up. But if you are just looking for good sound, then get different lengths.

Hide the extra cable behind the rack… or under the rack. This is what I always do.

When you are putting your new system together, if you can, I'd put the components on the side wall and use long RCA's to your amp placed on the fireplace hearth behind your speakers. I would never locate my components in the room's corner, especially the turntable. Too much potential for sonic degradation due to vibrations, etc. If that doesn't work for you, you might consider moving your speakers out further in your room and placing the components behind one of them and the running one of the cables around the base of the hearth. Differences in sound from cables of different lengths is more of a mental thing than a sonic reality. FWIW.

@ghdprentice   While I don't disagree with what you say, I worry about loops of cable are the basic inductor shown in any electrical physics book.   It is a small inductor, but it is an inductor.

No wrong answer here but I've been going with unequal length cable over coiled cable. 

Now if you can hide the extra cable without loops, then you have avoided both potential pitfalls.

Jerry

@carlsbad2 The floor is wood, unfortunately. I did think about getting one of those quarter-round wire hiding trim things to secure the wire in front of the fireplace at least, but I'm not sure I'll be able to find any big enough for the thicker cables. There might be some sort of little white bracket/clip thing i can install to hold it up off the ground along the top of the trim though maybe. Worst comes to worst it just runs on the floor, but I worry about it being a trip hazard, etc.

Yeah, there's some debate about varying lengths vs not, but really the only way to hide that much excess since it would be 6+ feet longer for the speaker further away would be to coil it and maybe zip tie underneath the rack. I think I would probably agree with you on varying lengths vs coiled.

@larsman I wish I had that option! The fireplace is used occasionally or else I'd just put the rack in the middle there in front of it. On the floor in front isn't really an option either since I have pets and the tubes would be a problem. 😅

@newbee Turntable will be against a wall on a rack, but not in the corner of the room. The furthest speaker away from the rack will be near a room corner, but not up against it - will be pulled out a few feet. I also plan on getting some treatment for behind the speakers as well. It's a bit of an odd layout with the fireplace off-center which makes this particularly annoying.