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.
Doesn't know if this is the real capacity but there is a custom 6600mah battery on ali express. Item: 1005004841020263
Asked the seller and the battery doesn't have protection board :/
Last I read Amazon owns some rights you'd think a billion dollar company could fork more over for a decent game but their last game bricked GPUs so theirs that