But you already KNOW what you want to do cannot be done with a six year old, 3rd gen iPad.
You really want an iPad with iOS 10 or 11, go out and purchase an iPad 4th generation or a new or refurbished iPad or another “newer” used iPad model capable of running iOS 10 or 11.
The older iPad 2, 3 and 1st gen iPad Mini will never, EVER be able to run iOS 10 or 11.
It is what it is.
Why do you need your iPad 3 to run iOS 10 or 11?
I have a seven year oldiPad 2 and I am still getting regular, daily updates of apps that I am, still using on my newer iOS 10 iPad.
So what app/s do you need that you need that you are not getting under iOS 9.3.5?