"Turn, Sinner, Turn O!" in Allen et al., Slave Songs of the United States (1867, pp. 36-37) was probably related to some versions of "Sinner Man" in the DT. Additional verses and comments below are from this book, too.

TURN, SINNER, TURN O!

1. Turn, sinner, turn to-day,
Turn sinner, turn O!
Turn, sinner, turn to-day,
Turn, sinner, turn O!

2. Turn, O sinner, de worl' da gwine,
Turn, sinner, turn O!
Turn, O sinner, de worl' da gwine,
Turn, sinner, turn O!

3. Wait not for tomorrow's sun,
Turn, sinner, turn O!
Wait not for tomorrow's sun,
Turn, sinner, turn O!

4. Tomorrow's sun will sure to shine,
Turn, sinner, turn O!
Tomorrow's sun will sure to shine,
Turn, sinner, turn O!

5. The sun may shine, but on your grave,
Turn, sinner, turn O!
The sun may shine, but on your grave,
Turn, sinner, turn O!

6. Hark! I hear dem sinner say,
Turn, sinner, turn O!
Hark! I hear dem sinner say,
Turn, sinner, turn O!

7 If you get to heaven I'll get there too,
Turn, sinner, turn O!
If you get to heaven I'll get there too,
Turn, sinner, turn O!

8. O sinner, you make mistake,
Turn, sinner, turn O!
O sinner, you make mistake,
Turn, sinner, turn O!

9. While de lamp hold out to burn,
Turn, sinner, turn O!
While de lamp hold out to burn,
Turn, sinner, turn O!

10. De wile' sinner may return,
Turn, sinner, turn O!
De wile' sinner may return,
Turn, sinner, turn O!

The following words are sung to the same tune:

1 Bro' Joe, you ought to know my name--Hallelujah.

2 My name is written in de book ob life.

3 If you look in de book you'll fin' 'em dar.

4 One mornin' I was a walkin' down.

5 I saw de berry a-hinging down.

6 (Lord) I pick de berry, an' I suck de juice.

7 Jes' as sweet as de honey in de comb.

8 I wonder where fader Jimmy gone.

9 My fader gone to de yonder worl'.

10 You dig de spring dat nebber dry.

11 De more I dig 'em, de water spring.

12 De water spring dat nebber dry.

[This is the most dramatic of all the shouts; the tune varies with the words, commonly about as given above, and the general effect is very pathetic. The words and tunes are constantly interchanged: thus, for instance, the 6th verse might be sung to the second variation, and the 8th, 9th, and 10th, to the third.]

Masato