I noticed today they’ve added the ability to link your stats to a NYTimes account, including a free account. So you can either log in or create a new one and then you’ll be able to create a new Home Screen favorite from the proper link, log in to the account, and have your stats.
Done! I’ve made a new Home Screen app and it has my stats. Including my streak which apparently wouldn’t get transferred with the method @raykloss found. Now we’ll see how much junk email NYT sends me.