I do not have an answer to your question Alex, but the more I look at it, the more curious it all becomes.
If you look at Figure 3 in the AP3456 you will see that piston best ROC speed is slightly more than Vmp. But if you turn the page to Figure 4 you see two different situations. The low altitude curves show best ROC at a speed lower than Vmp, but the high altitude curves show it at slightly higher than Vmp. I suspect that this is simply an error and the author was concentrating on showing how the speeds vary with altitude, rather than showing their relationship with Vmp.
Eshelby's Figure 3.18 is curious in that it shows the thrust available curves as being convex to the origin. This is contrary to those in most other texts (every one that I have seen). Most texts show the thrust curve as being concave to the origin at the low end of the speed range and becoming slightly convex to it only at the high speed end. Also if we take his thrust against EAS curves from figure 3.18 and multiply them by increasing values of EAS (to get thrust power) we will not get the straight lines for thrust power against EAS, shown in figure 3.19.
If as Tinstaafl suggests, Eshelby has normalised his thrust power curves in Figure 3.19, then surely he should have also done this to the drag power curve, so that their relationship was not distorted. He does not appear to have done this, and perhaps this is the cause of his curious result of having best ROC at Vmp.
I suspect that like the author of the AP3456, he was concentrating on showing one aspect of the subject (Excess power = thrust power - drag power) and in so doing, inadvertently introduced an incorrect relationship between best ROC speed and Vmp.
Figure 3.19 is also curious in that the author has used the term "Maximum excess drag power" to represent thrust power minus drag power. Surely this should be "Maximum excess thrust power".
Hmmmmmm.....curiouser and curiouser.