Hats off to those who found the play. David Rockwell has rolled this one and agreed to extend it to 31k so we get a vigorous rollout (thanks!). I also add the XG++ evaluation for comparison.
My thinking was that 13/9 is mandatory. Then I play 18/10 to safety the checker. For the last 4 I was thinking of 13/9 as it seems that the spare is more efficient on the 9 pt than on the midpt for the potential to extend the prime and make an inside pt next. My second choice was to play the last 4 as 24/20. The top play wasn't on my radar as it seems against my understanding in general and the opening in specific: We have a race lead, strong prime potential and weaker board. These should suggest to a safe play, i.e., avoid direct shots, while in the process we get a good structure. Its not like we don't have alternative constructive 4s.
I still don't understand the logic behind the top play although some of your arguments have helped. I think this is an unusual play and you should be careful about generalizing from this rollout. If you want to infer from it take the basic  in the early game, when the opp has anchored on the 22 pt, the 9 pt has higher value than the 5 pt. This generalization (with some exception) should be clear to strong opening players but may be worth pointing to others.
I am wondering whether there can be a 3ply misplay that leads to a consistent bias in the rollout. The equity for the top play has jumped by 0.03 which is unusual for an opening play rollout (for money). Is it worth rolling with higher settings? If not, why should we volunteer a double direct shot in front of the opp's most stacked pt when I am ahead in the race and outboarded??!!
  White is Player 2
score: 0 pip: 159  Unlimited Game Jacoby Beaver  pip: 157 score: 0
Blue is Player 1  
XGID=bECAeDcAcbA:0:0:1:44:0:0:3:0:10 
Blue to play 44 
1.  Rollout^{1}  24/16 18/14 13/9  eq: +0.130 
 Player: Opponent:  54.79% (G:7.97% B:0.33%) 45.21% (G:12.27% B:0.39%)  Conf.: ± 0.003 (+0.127...+0.133)  [100.0%] Duration: 6 hours 56 minutes 

2.  Rollout^{1}  24/20 18/10 13/9  eq: +0.097 (0.033) 
 Player: Opponent:  53.25% (G:10.83% B:0.44%) 46.75% (G:12.43% B:0.42%)  Conf.: ± 0.003 (+0.094...+0.100)  [0.0%] Duration: 6 hours 28 minutes 

3.  Rollout^{1}  18/10 13/9(2)  eq: +0.091 (0.039) 
 Player: Opponent:  52.65% (G:11.50% B:0.48%) 47.35% (G:11.77% B:0.44%)  Conf.: ± 0.003 (+0.088...+0.094)  [0.0%] Duration: 6 hours 09 minutes 

4.  XG Roller++  18/6 13/9  eq: +0.007 (0.123) 
 Player: Opponent:  51.05% (G:9.99% B:0.37%) 48.95% (G:12.63% B:0.39%)  

5.  XG Roller++  18/14 13/5 9/5  eq: 0.014 (0.144) 
 Player: Opponent:  49.72% (G:11.03% B:0.38%) 50.28% (G:11.78% B:0.41%)  


^{1} 31104 Games rolled with Variance Reduction. Dice Seed: 17881389 Moves: 3ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10
  White is Player 2
score: 0 pip: 159  Unlimited Game Jacoby Beaver  pip: 157 score: 0
Blue is Player 1  
XGID=bECAeDcAcbA:0:0:1:44:0:0:3:0:10 
Blue to play 44 
1.  XG Roller++  18/10 13/9(2)  eq: +0.101 
 Player: Opponent:  52.86% (G:11.24% B:0.44%) 47.14% (G:11.17% B:0.38%)  

2.  XG Roller++  24/16 18/14 13/9  eq: +0.097 (0.003) 
 Player: Opponent:  54.58% (G:7.63% B:0.28%) 45.42% (G:11.64% B:0.35%)  

3.  XG Roller++  24/20 18/10 13/9  eq: +0.087 (0.013) 
 Player: Opponent:  53.19% (G:10.65% B:0.41%) 46.81% (G:11.89% B:0.37%)  

4.  3ply  18/6 13/9  eq: +0.024 (0.077) 
 Player: Opponent:  51.49% (G:10.02% B:0.29%) 48.51% (G:12.08% B:0.32%)  

5.  3ply  18/10 13/9 6/2  eq: +0.011 (0.089) 
 Player: Opponent:  51.04% (G:11.13% B:0.36%) 48.96% (G:12.98% B:0.44%)  

eXtreme Gammon Version: 2.10