I’ve got a cold and I have brain fuzz. David Prosser passed on this wonderful info in comments so I thought I’d give it its own post. The number below is a phone no. Apparently you can use it to get an EIN over the phone. Thanks David!
1-267-941-1099 The option you want is the first No 1. I was placed in a queue for 15 mins and then it took 14 mins to get my EIN ! No passport, no ID, no company, just very easy.