To clarify, when booking dining reservations you can book at 11am (UK time) on the app and midday (UK time) by phone. depending on what date you are booking, remember that the clocks change later this month so the time difference might be slightly off. It is 6am and 7am Eastern (Florida) time respectively for online or phone bookings. You might find it easier if you have your credit card lined first but as you aren't trying for anything particularly hard to get, then it probably won't matter if you don't have it linked.
For FP+ reservations, ChipandDaleRule is right, you can book these at midnight Eastern (5am UK time). But unless you want Anna & Elsa I would not bother getting up that early. I had no trouble getting 7 Dwarfs Mine Train twice for my trip later this month and didn't make our FP+ reservations till about 6am.
ETA: It looks like our clocks go back on 26th October so, for another week (until 2nd November), we will be only 4 hours ahead instead of 5. So, if you are booking between 26th October and 2nd November, you will be able to book at 10am online and 11am by phone.