Ah. So I'd come here if I wanted information from other users who have had the same problem. Which is why I came here in the first place.
So far, I've reset all the Bluetooth connections in my house and have had luck with gaining distance again. Anyone else who doesn't just want to ship their console off for some unknown amount of time with no replacement to borrow maybe try the Bluetooth thing - wireless speakers, phones/tablets, wireless keyboards/mice. Turned off all Bluetooth, unplugged WiiU, reset Gamepad and got most of the functionality back at good distance. Turned everything back on and we're good.
So am I to understand that the Gamepad sends a Wi-fi signal to turn the WiiU on? I've been able to turn it on at just about any distance, even if it doesn't connect. That means it's two different wireless signals to power up from the Gamepad and to connect to the Gamepad, right?