Plugging in the following numbers in the lineup analysis tool (OBP/SLG):
Heyward .350/.400
Justin .375/.500
Freeman .390/.500
Gattis .290/.500
BJ .290/.350
CJ .320/.320
TLS .350/.350
Simmons .300/.400
pitcher .150/.150
and throwing out any lineups where Freeman bats leadoff, the top lineups are:
4.442 Heyward Freeman CJ Gattis Justin Simmons BJ pitcher TLS
4.442 Heyward Justin CJ Gattis Freeman Simmons BJ pitcher TLS
4.441 TLS Freeman Heyward Gattis Justin Simmons BJ pitcher CJ
4.441 TLS Justin Heyward Gattis Freeman Simmons BJ pitcher CJ
4.441 Heyward Freeman TLS Gattis Justin Simmons BJ pitcher CJ
4.441 Heyward Justin TLS Gattis Freeman Simmons BJ pitcher CJ
4.440 Heyward Freeman CJ Gattis Justin BJ Simmons pitcher TLS
4.440 Heyward Justin CJ Gattis Freeman BJ Simmons pitcher TLS
4.440 TLS Freeman Heyward Gattis Justin BJ Simmons pitcher CJ
4.440 TLS Justin Heyward Gattis Freeman BJ Simmons pitcher CJ
4.439 Heyward Freeman TLS Gattis Justin BJ Simmons pitcher CJ
4.439 Heyward Justin TLS Gattis Freeman BJ Simmons pitcher CJ
4.439 Justin Freeman CJ Gattis Heyward Simmons BJ pitcher TLS
4.438 Justin Freeman TLS Gattis Heyward Simmons BJ pitcher CJ
4.437 Justin Freeman CJ Gattis Heyward BJ Simmons pitcher TLS
4.437 Justin Freeman TLS Gattis Heyward BJ Simmons pitcher CJ
4.428 Justin Freeman Heyward Gattis TLS Simmons BJ pitcher CJ
4.427 Justin Heyward CJ Gattis Freeman Simmons BJ pitcher TLS
We can immediately throw out any lineups with CJ in the top half, realize that Justin is not leading off, and remove any with the LHers hitting 3 in a row, leaving us with:
1) 4.441 TLS Justin Heyward Gattis Freeman Simmons BJ pitcher CJ
2) 4.441 Heyward Justin TLS Gattis Freeman Simmons BJ pitcher CJ
3) 4.440 TLS Justin Heyward Gattis Freeman BJ Simmons pitcher CJ
4) 4.439 Heyward Justin TLS Gattis Freeman BJ Simmons pitcher CJ
It's pretty clear that Justin hits 2nd, Gattis hits 4th, Freeman hits 5th, Simmons and BJ hit 6/7, pitcher hits 8th, and CJ hits 9th. The only postions that are unclear is TLS or Heyward in the 1and 3 holes, so I personally stick Heyward in the 3 hole and go with option #3. If someone has a major fit about the pitcher batting 8th, go ahead and slot CJ between BJ and Simmons.