By themselves the scenes made for good eye candy. Product placement was a tad over the top.
The arrangement of "happy together" was embarrassing but a perfect complement to the "story".
To improve your live audio on a smaller scale I'd encourage you to record live music with just the on board mics on the H4n. Experiment moving the mic placement and with stereo width (twist the mics).
Listen to the recordings and try to figure out what's too soft or too loud. What instruments get washed out from untamed room reflections? Experiment with adding a single mic, then two. Then, go back to the console and see what you can get from there.
Specifically the Yamaha mixer you mentioned in the original post is more than capable of creating a separate mix for recording. Moreover the mix can be controlled by an iPad.
Honestly though, you'll likely fare best with a minimalist approach. How would you answer someone asking how to be a better editor and color grader?
Excellent point and applicable beyond screenwriting. I'm going to email and post links to the article on social media. ;-p
As another person responded make certain your levels are good. With the H4n it's a good idea to use as little on board gain as possible. A good signal from the sound board will mean you can leave the inputs turned all the way down. It's important to know the gain structure of your recording chain.
Chances are you'd actually get a better recording using just the mics. I'm making the assumption this isn't a 4,000+ capacity venue and a lot of the sound getting to the audience is from the stage sound itself. A live sound engineer is naturally going to have proportionally more vocals in the PA than drums since the drums are naturally acousticly louder. In that case a feed from the PA will have loud vocals and little in the way of drums except what's picked up in the vocal mics. Often guitar players will have their amps so loud that they aren't even in the PA. In most small venues there's no drum overhead mics and the PA's version of the drums will be just what's needed to beef up the sound to compliment the natural sound in the room. I could go on...
When a live performance is recorded professionally a "splitter" is used. Mics are fed to a recording board and live board independently. Also, extra mics are frequently added that the live engineer doesn't use at all, like overheads, bottom mic on snare, etc....Ohhh and don't forget the audience gets mics and mics to capture the room ambience....
often PAs are mono, especially in smaller venues. The stage sound provides surround sound ('cause it's real). You might be able to record dual mono for a safety track, or devote an extra input to an audience mic. Finally, most boards have more than one mixing bus. What that means is sometimes you can get a custom mix strait from the board, tailored just for recording. Most of the time though they are used for monitor feeds and effect sends.
Some boards feature wifi and have accompanying ios/android apps for a band member to mix their own monitors. If you get lucky you might be able to get exactly what you want and stay out of the engineers way.
Finally, musicians and engineers can't resist knob twiddling. A mix will change over the course of a performance.....