The Brazilian paper from 2016 you cited has a lot more on the action and functions of turning: here are some highlights
"Egg turning is a natural behavior of birds during incubation, and therefore, this practice was included in the artificial incubation process. Egg turning allows the diffusion of gases inside the eggs and between the eggs and the external environment. It is critical particularly during the first week of incubation, due to the long distance between the embryo and the shell, and to the high albumen density. During this period, the embryo depends on the diffusion of gases through the eggshell and the albumen to obtain O2 and eliminate CO2, because the embryo develops on the yolk surface and gases are exchanged directly by the embryonic cells. ... By days 13-14 of incubation, fetal metabolic heat production increases, and egg turning aids the circulation of air in the inner surface of the egg (external shell membrane) and air chamber, and allows heat loss by conduction, convection, and evaporation. However, egg turning is also important to prevent dehydration and incorrect embryo development (Wilson, 1991). Moreover, egg turning moves nutrients, facilitating their absorption (
Brinsea, 2006). Egg turning is not as simple as it may seem. Egg turning frequency, axis of setting, angle, and plane of rotation influence in-ovo development, which may affect hatchability and chick quality (Wilson, 1991). Landauer (1967) demonstrated that chicken hens turned eggs approximately 96 times daily during natural incubation. ... During natural incubation, eggs are often exposed to temperature fluctuations in the nest, which may be caused by environmental temperature variations or changes in the attention hens direct to the eggs. Before the complete development of the chorioallantoic membrane, around day 12 of incubation (Tullett & Deeming, 1987), the embryo responds to the temperature gradient between the egg region in contact with the hen and the part of the egg in contact with the nest material, directing the blood flow to the colder region, regulating its internal temperature (Tzschentke & Nichelmann, 1997). After the complete development of the chorioallantoic membrane, the