My immediate impression of this song was acoustic bass, and percussion = congas, bongos and a soft felt-batted kick drum to give gentle at the bottom. I’m learning percussion, which motivated my thinking in this direction, however I am not good enough to provide better than amateurish. However, I decided to, at least, mention the idea and give my reasoning.
As I think of a kick/snare/hihat based kit, I’m thinking it could be harder to ‘glue it’ into what there already is. Why? The vocal is incredibly dense: melodically, tonally and rhythmically as well as lyrically, it is putting important meaning in all the places that sharp sounds would interfere. I notice how the guitar seems treble cut until the very last chord. I thought it was a nylon strung until then - though I might be showing my general ignorance of acoustic guitars. The ‘comfortable pops and bums’ of congas would sit with that guitar and allow that voice the space it needs. Bongos could add a little salt an pepper in big gaps, or where voice leaves a lot of space for something to counterpoint. In my mind’s ear, I had a quick listen to a snare drum with brushes. Didn’t seem to work as badly as snare with sticks.
In order that you get a sense of where I am standing as I wrote the above:
1: I was envisaging a final product in which those two tracks you shared [voice and acoustic guitar] will be pretty much unaltered in the final version, and that Only bass and drums is to be added.
2: I got strong and immediate resonances with Joni Mitchell and Joan Armatrading. Both of them wrap tone, melody, timing and lyrics into a dense-weave cat’s cradle. It is an acrobatic gravitas, a complexity without confusion or gimmikyness which, within 5 seconds of his starting to sing, filled me with an appreciation of and trust in your vocalist.