I've said it before but if you just want a quick and convenient way of boosting the battery capacity there's plug and play batteries you can still buy from China/iFixit/Amazon.etc
The point of this is it's a DIY modification showing that for around £20/$20 along with some time and effort you could have a ridiculously large battery... if that's not for you, then go buy the Wii U battery and save yourself the hassle.
After carefully reading your post I got really afraid of doing the mod. The battery is here, I have a spare battery, but now I'm thinking of returning the battery to the seller. I'm afraid the battery can explode on my gamepad.