Matt, yes it does appear that you're making this more complicated than necessary. A balanced 2-conductor connection using XLR at each end can have greater interference(hum)rejection than coaxial cables with RCA plugs at each end, but this would be meaningful only in the presence of unusually high interference levels which usually don't occur in typical home installations. The usual shielding in coaxial cables is entirely sufficient for such installations.
Also, as the previous reply touched on, a balanced connection requires a balanced output in the first unit to send out two signals(but reversed in polarity)rather than the one signal carried by the one center conductor in coaxial cables. A single output, such as the one from your receiver, can't do this and using an RCA to XLR cable makes no difference.
While gauge is a significant factor in long runs of speaker wire it is of no significance in low level interconnecting cables. RG6 is unnecessary for such use and I use the thinner, more flexible RG59. If you need 3 foot cables these
should be satisfactory.