Hello Caleb - I ran into a similar situation here within the 1st few weeks of a new iPad. Long story short, the A1474 digitizer is compatible, but the button is not. The touch ID is synced with the ribbon and the mother board. The older iPad Air (A1474) button is not recognized by the newer iPad A1822. If the button is damaged there is no way to repair it at this point. The best you can do is not to tamper with it and return it to either Apple or an authorized repair shop for a new machine which will cost $249 if still under warranty. You can find those locations here: https://locate.apple.com/ As soon as it has been worked on, the warranty will be voided and you will not be able to receive the discount. When a solution for the button goes onto market, then it may be worth repairing this independently. Hope this helps!
Hello, ran into this same issue and here is what I found: Basically the digitizer works, but the button does not from the iPad Air 1st generation. Read my full post here regarding this same question: Replacing/Repairing Home Button and Cables for iPad 5
A quick follow up to this - I ordered an iPad Air 1st generation (A1474) digitizer and button combination pack for this. Everything works except for the button. It appears that the syncing of the motherboard, the button and the ribbon disallows the button to communicate with the motherboard and the monitor. A $30 experiment here to see if this is the case or not. So, long story short, when doing this repair, make sure the button and the ribbon to the button are not damaged, or it will be impossible to repair at this point (until a 3rd party solution is created for the button on this model). This was not true with prior models so important to know when working on these machines.