Second model of the pile cap with piles modeled as spring node supports. for moments and shear forces calculation, the reactions of the piles agree also very good. Moments and shear forced on the other hand not so much.
My understanding is we have already covered this topic.
The pdf file racomends to use beams as idealized grillage elements in order to find the moments and shear forces for reinforcement design of the pile cap.
and this is the model from the post 15 whereas yours is similar to the one from post 17. As you can see the later includes bi-directional behavior of the panel which influences the results. These are two different models (compare values of shear forces 1425 vs. 1018 for the same load) and for the book 'approach' you should create a number of beam type models rather than a panel one.