I agree with longtimedisneylurker that the easiest option is to watch the first showing a F! and then view the fireworks from that area (just make sure you are in a position to see the mist screen and the fireworks at the same time, so try to make sure that the mist screens are between you and Big Thunder). You'll miss out on the Main Street projections (which differ from the ones on the castle and the mist screens), the flying characters (you can see them, but not how they're framed in the show), the special effect on Main Street, and some of the on-the-castle effects. You'll still get a sense of the show, but I do think you'll miss out on a lot of the "immersive" elements/feel to the show by watching it from the Rivers of America area. Personally, I would watch the fireworks from this area as a second choice, after you've already seen it from Main Street.
I would consider looking into doing one of the dining packages for the second F! showing and then watching fireworks from Main Street. After fireworks ends, head over to the F! viewing area. It'll be slow going but if you have a dining package FP, you will probably still end up with a good view when you get over to the viewing area. That being said, you will probably be towards the back of the reserved viewing area for the dining packages, but given that it's usually ground seating, the view is typically pretty good from anywhere in the section (just try to avoid sitting behind someone markedly taller than you).