I find different devices have never done much for me, so I'd use the device you are most comfortable with. Be where you have a good wifi/internet/cell signal!! I then prioritize the ADRs in order of importance and popularity - if we are staying at a WDW resort, we might push a popular ADR to later in the trip so you can improve your chances at 60+4 or 5 or 6 days. We'll put something a little simpler earlier in the trip. I handle them all myself, since my account tends to be the coordinator of our tickets, room reservations, ILL/G+, dining etc. We've not found a big advantage to 2 of us being on, but maybe others have.
Maybe get up early a morning or 2 this week and do a practice run. You'll only be able to see what's available 60 days out, but it might give you a little more comfort when you do it for real on Saturday. Good luck and have a nice trip!