I run 10ga as well, and use two methods to conceal wires.
The first is that rubber floor strip used for office floors, which works in one location because it reasonably matches the tile surrounding my fireplace:
The second is an home made oak strip, made from two pieces of 1" thick solid oak flooring of the same pattern and vintage of the floors in my home. Basically, I glued and fastened two strips together before bevelling and making dado cuts on my table saw. The dados are big enough for two 10 ga wires to pass underneath.
I'm reasonably certain that the same thing could be constructed from modern composite veneer flooring, which typically has an MDF underlay. The only thing you'd need to do is use a laminate blade for the bevels and stain one shade lighter (fresh cut MDF takes stain very well, so it tends to react with darker color).
As for back of the rack, previous suggestions wrt Velcro straps make the best sense. Just keep power cords and source/speaker wires separate. If you need to cross them, try to do so at 90 degrees to avoid induction issues.
