Again, take what I say with a few pounds of salt, as my perspective is just what it is. A perspective....
In a video, that talent you got there, playing and singing a whole song, in a single take, isn't of much importance. Once you make it big, then yes, it becomes very important when playing live. But in a video you're telling me a story. A visual one in your case. As the main carrier for your message (which in your music is an emotional one) is how pleasant you sound and look, with the lyrics taking a much less important role. It doesn't matter how many takes you record. In fact, they are welcome. Changes in scenery, view angles, grading, etc will only keep me interested in what comes next. Something as simple as you walking around the park, or sitting in a bench singing, or the beach, whatever... A static background isn't going to grab much attention.
Some singers could really just be sitting in a toilet, and we would still be watching them. But those have their lyrics as the main carrier for their message. Tim Minchin comes to mind...
Unless you have 2 good mics, I'd record the guitar and voice separately, and make them sound as good as you possibly can. Then, film myself singing in a whole variety of places. And finally, make an edit of my favorite clips and put them together. Filming techniques, and editing can make your message go from 1 to 1000 in a big hurry.
I like your "broken" video.
Nice control of your voice as it's clear you could really belt it out if the song called for it. Wasn't even sure if you were really playing the guitar at first since it's just out of frame haha But upon inspection, your skills on that are impressive as well. Nice backdrop as well.
