Rob, the book has it written out in the key of Aflat (Ab). What key are you tabbing/playing it transposed to?
Here you can buy/listen to the song transposed to key of C (with I think an accidental Bb not in it- (not 'accidental' as in 'mistake'). The sample clip starts within the first whole measure of the more tricky B part (second part) BTW.
Probably worth buying the whole album. It has more than one song from the "Slave Songs" book, which has a large number of gospel songs in it.
--- IF you are trying to play the B part in the key of G (which has one #...F# in it), then that phrase the the sample clip starts with would be the notes: D-F#-D-F(F natural)-G-E (these notes corresponding to the lyrics "I do believe.. We're a " Hope this helps?
I'd recommend you go into Briggs key of G simply to make it simpler to figure this song out. After you have it tabbed out or can play it by ear, then you can tune all your strings up and down and see if it plays ok from there.
Remember, simply changing the pitch of a tuning evenly across all strings (like going from eAEG#B -"low bass" key of A...to dGDF#A -"low bass" key of G) doesn't change your fingering. But changing the actual intervals between the strings- changing to a 'different' tuning (as in low bass vs high bass) DOES then change the fingering and often the key, and it very much effects what finger moves and sharps and flats you might need to play for a tune. Could make it difficult or more easy.
It wouldn't make it 'easier' simply pitched down a half step from eAEG#B to Ab... you'd still be using the same fingering as any low bass tuning, like Briggs in G or A. It'd just make it harder to help you when we're referring to the notes. ;)
So purchase Andrew Calhoun's sung version (for 99 cents if you don't want the whole album), and use some software like Amazing Slowdowner to change the key from C (the key he is singing it in) to other keys you typically use on your banjo... and pick out the melody on your banjo to see if it lies better in G or D on your Briggs-tuned banjo.
i don't think I'm too far from it. It's just little twiddly bits to keep it from sounding so droll. I typically need both the tab and to hear it and go from there. In typical folk songs, you can get away fudging some things or "making your own version. But with a lot of the minstrel music (esp the books -- Briggs, Converse, etc), you can't quite afford to do that.
Particularly in this tune, it's the odd or unexpected phrases and notes (the ones that don't go where you normally would expect them to) that are essential to give the tune its unique character and identity.