I've thought about that as well. Varmint AI talks about stock stiffness in his Estens rifle page. What he is saying it does is it delays the barrels response to recoiling into the stock.Well, I suppose I can add to the confusion or the question at hand. it is my finding that the barrel may play a small role or even a larger roll in what I call static pre-_load to the stock or platform while laying in battery in a natural state, how much pre-load naturally depends on weight of barrel and length I suppose. but more direct to your question what builds ladders that trend down before trending up while increasing charge is a direct link to how soft or flexible a stock is. softer stocks will resist vertical climb for a given charge window vs there stiffer counter parts I find they simply ladder differently. it is my opinion from what i see in a soft stock that it will hold a natural center or point of aim before bouncing up the page now if two soft in the horizontal plain you will see more horizontal dispersion but with the correct combination of both will make a excellent platform. as i increase charge the stock will see more force under recoil compressing stock down hence the point of impact trending down first before springing up the page.
Shawn Williams
Vaughn said something similar though he put a literal shock absorber in between his stock and recoil lug.
I'm assuming a similar effect could be achieved with a stiff stock and a very soft recoil pad. Though that may depend on the weight of the stock. Light and stiff might work but heavy and stiff probably would not.