To be honest, I really wouldn't worry about it.
They are pretty much universally friendly and helpful. If you call up on the wrong frequency, they will soon have you on your way...
Just so you know, under the hood, SkyDemon have mapped all the FIS sectors. So when you tap the button to bring up the frequency list, the one at the top will always be the correct one. When you are within a few nm of a boundary, it will show both.
Sorry about that chart, but it's the only one I know with all the frequencies, and I too had missed the little insert at the top right... Just print that as your backup
Another thing to consider for your trip is to use the class 'E' airways. You can do a pseudo IFR flight that way routing along the airways. For a non IR pilot like myself, this was good fun.