On an update to my splitter questions and upgrading notes:
I have removed three 4-device AV splitters from the set-up, and replaced them with one (eventually two) 8-device switches. I found one on Amazon that is remarkably sturdy and well-made. It currently has NES, SNES, N64, GameCube, Genesis, Saturn, Dreamcast, and 3DO plugged in.
Currently, the PS1, PS2, PS3, Ouya, Xbox, and GameStick (GameStick is also not in the console database on the site, and maybe there should be an Android console section to include this, Ouya, Shield, and Fire TV) are not plugged into the main set-up. The secondary TV still utilizes coaxial input games, but I moved the NES to the plasma TV, cleaned it with ye olde fashioned NES cleaning kit, and finally it seems to be working as expected again.
I have essentially confirmed that the receiver badly needs the capacitors replaced, as it is very slow and chunky to switch HDMI ports. However, the Wii U runs quite beautifully on the HDMI now.
I removed nearly a dozen cables from behind the entertainment center.
I discovered an anomaly I did not consider before. I purchased an unpowered HDMI splitter and discovered that only the Wii U is able to punch through it with ease. The PS3 can't get a signal through it at all, and the X360 can't play DVD's through it, but can play games. Go figure. I will have to upgrade to a powered HDMI splitter from here on. Eventually.