Sawmill (also called mountain minor) brush will sound off because the C on the 2nd string does not fit in normal chord intervals for the G chord. It's not supposed to :-). Mountain musicians did all sorts of things with their songs to make them sound weird/better/less sweet/take your pick. For instance, some intervals between notes were 1/2 a semitone (can only easily get that with a fretless instrument; fretted banjos can use a bend on the next lower fret to get the 1/2 semitone effect; I've never done it, only read about it, so not an expert).
If you want a more harmonious brush, leave a finger on the C string at 2nd fret, making it a D, giving you a 1-5 power chord with your brush.
Another thread on BHO tunes to a true Gminor key, dropping the C into Bb. You might try that tuning with your song.
Audacity allows me to slow any downloaded song to the speed I wish; I do it all the time for learning a song by ear. Audacity, a freeware program (donation accepted) will also change the key of the song, independently of changing the speed; again, I use it all the time to put the song in a key (tuning) I like.