Aw, Don't fret too much - it can sound like a big deal, but aside from the few big ticket items most things will be easy to get.
The divide and conquer technique on two devices is a great idea - and will not cause any issues.
I just would not both work on the same day or it might get confusing with overlapping times.
One thing I would suggest (even if you are using a single device) is to log out of Disney site about 1/2 hour before, clear your browser cache, restart the browser and then log back in about 10 or 15 minutes before.
It can be a wonky site sometimes and that technique Might help, Can't hurt.
What I do is create a simple table in a spreadsheet where I can keep track of what I got so I don't overlap things. There's a screen capture of my table below... In the table I also include the park hours (made the EMH times red), plus my current Dining Reservations so I don't try to get a FPP to close to one.
As I get them, I type in the name and time so I know to look for the next one at least an hour later.
I also made a little checklist for the hard ones I wanted to get first - I did those in reverse order from hardest to get hoping to insure I had a better chance for those. Then I just went back and did the rest in chronological order - no issues with anything.
My hard to gets were:
FoP on Monday
7DMT on Wednesday
PP on Friday
Soarin on Thursday
Then I went back to Monday and did the rest in order.
I did NOT get FoP even though it was 7AM at 60 days, but I did get NRJ. It took my about 4 or 5 weeks of browser refreshing to see a set of FoP and I modified NRJ to get them.
Everything else was a piece of cake. Worst case scenario: things open up all the time with most FPP, all the way up to the date you are going. We made a few ADR and plan changes over the course of time, and I had no trouble modifying anything to a different time, (except for FoP of course.)
BTW, On the day in park, remember that as you use your FPP, you can go right into MDE as soon as you pass the tapstile and try to modify your next one to a better/closer time if it might help you or after your 3rd one is done, look for a 4th FPP.