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In the third roll position above right, Blue has pre-escaped with 65R. In this case, with one checker back, it becomes better to play K (hit twice). The value of unstacking the sixth checker on the midpoint (mentioned by a couple of respondents) is overridden by the incentive to reduce return shots with a race lead and only one checker back: [K H14] "<15. Overall, it's a swing of .059.
I rolled out the fifth roll variant 65R-43Z-31P-42P-32, below left. It is the same as the third roll position, except Blue has made his 5pt with 31 and White has made her 4pt with 42. Now it switches back to H being the better play: [H K21] "<5.
Why the switchback (of .035)? I believe the key reason is that Blue has one fewer checker on the 6pt -- for example if he subsequently uses it to cover his 1pt he is out of spares. If you alter this variant by giving Blue 13/6 (and give White 13/6 as well to keep pace in the race, if you like), I'm sure that K (hitting twice) would be best for reasons discussed in my second paragraph.
Finally, your sixth roll position 41S-65R-42P-31P-52Z-32 is shown on the lower right. H wins by even more because Blue is relatively 5 pips worse off in the race (by virtue of White's extra 13/8); he is motivated to play more purely. It turns out that XG's 4-ply eval is reliable but I rolled it out for more accuracy: [H K38] "<5.
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Nack