...needing a gammon, 6/5 seemed like a better bet. Rollouts show that although 6/5 gains over 24/23 at Gammon Go, the gain is almost negligible.
Based on rollout difference, comparing the money margin to the gammon go margin, it improves for N (Near, 13/8 6/5) versus S (24/23 13/8) by .005 or .006 against White's 5pt or 4pt position (or by .007 against White's 3pt position, based on evals). Your direction is correct; it's just that your expectation of the adjustment was too high.
White's back checkers are not split yet, so the possibility of blitzing is more remote. Also, 6/5 only diversifies a spare; it doesn't add one. Consider, too, that whether White is split or not, the second spare on Blue's 6pt often works out better with some doublets (2s, 3s, 4s, 5s), which overall dilutes some of the diversification gain. (If there were a fifth checker on the 6pt, the 6/5 ace would be more efficient.)
I knew that 31P-31P-51 was almost dead even [for money]. I judged (mistakenly, as it turned out) that his 42P (instead of 31P) made me very slightly less inclined to split due to advantage of 42P over 31P in 2 pips and due to his slightly worse priming position compared to 31P-31P-51. So, I am still scratching my head here wondering what is wrong with my thinking.
Your befuddlement is understandable, because on the surface your logic is correct. In general, against positions with greater priming potential, there is a commensurately greater motivation to split.
Assume that as Blue, because of your stripped 8pt, you should automatically play your 5 down (13/8). This will make it easier to focus on the ace.
The analysis that follows will be much easier to comprehend if you can widen your screen to fit each pair of diagrams side by side.
White owns the 5pt in the upper two positions (diagrams A and B).
White owns the 4pt in the lower two positions (diagrams C and D).
Blue has played 24/23 in the left-hand positions (diagrams A and C).
Blue has played 6/5 in the right-hand positions (diagrams B and D).
In general, the higher White's inside point, (a) the worse you are primed, and (b) you're 2 pips (per point) better in the race. For both (a) and (b) reasons, Blue has more incentive to split (24/23) against White's higher point. That logic is valid, even though there may be offsetting reasons that are greater.
Let's examine the rollout information:
Versus 5pt, play 24/23 by .009
Versus 4pt, play 24/23 by .020
Versus 3pt, play 6/5 by .001
As you can see from the above three lines, normal expectations have been met when comparing the effect White's 3pt vs 4pt, or White's 3pt vs 5pt, but there is a "hiccup" when comparing the effect of White's 4pt vs 5pt. Why? Analysis continues below the 2x2 diagram matrix.
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The two salient ones in this case appear to be double 4s (44) and double 1s (11). To wit:
Double 4s: Against the 5pt, 24/23 as in Diagram A gets punished when White hits while making a four-point board. If you could somehow divine that White will roll 44, you would clearly want to dodge this by playing 6/5 as in Diagram B.
That doesn't happen when you split against the 4pt in Diagram C. There, White's 13/9(2) 6/2*(2) also hits but makes only makes a three-point board. Instead, White will presumably make the 5pt (13/5(2)), at which point there's not much difference whether you played 24/23 as in Diagram C (back on roll, the ace-split offers you both pros and cons) or 6/5 as in Diagram D.
Double 1s: Splitting becomes a big gain for Blue when White owns the 4pt (in Diagrams C and D), because 11 makes both her 7pt and her 5pt, building a four-point prime. In Diagram C, Blue's leading back checker will eye direct 6s (23/17) for escape. By contrast, in Diagram A, with 11 White must choose between making the 7pt or the 4pt (she cannot do both).
Double 2s and double 3s should be routinely compared as well, but for this (5pt/4pt) pair of positions, I believe the net effect is a wash.
White's single roll of 42 (especially as it is a non-doublet) is twice as likely to be rolled as a doublet and argues strongly for splitting against the 5pt. However, her roll of 31 argues strongly for splitting against the 4pt. The effect of these two rolls is a wash, too.
Worthy of examination are 61 and 64. I think the net effect of these two rolls is also a wash.
Finally, there are all the other White rolls. Most (if not all) of them slightly favor splitting against White's 5pt more so than against her 4pt (by mainstream reasoning), but in the broader scheme all these rolls put together are dwarfed by the immediate impact of double 4s and double 1s.
Hope that helps.
Nack