The process of transition away from Hinduism was gradual, and also not total.

First, it's important to note that while the "rise" of Buddhism was complete sometime in the 15th century, Buddhism was not new in mainland Southeast Asia. Evidence of Buddhism is found in what will become the Khmer Empire dating from shortly after the Ashokan period. This is not surprising, since the same linkages which created the Indianized kingdoms of the region brought Buddhist missionaries alongside Hindu influences (with the disclaimer of course that "Hindu" influences are themselves a wildly diverse category).

This introduces the first wrinkle in answering your question, which is the distinction between elite and popular religion. Because while it is clear that local rulers practiced a syncretic form of Hinduism and indigenous Khmer religion, it is more difficult to tease out the practices of common people. Since popular religion is less likely to be preserved than large stone monuments, all we can say is that we know Buddhism was present as part of the pre-Angkorian and early Angkorian religious milieu, but it is difficult to say at what levels.

Second, the transition was not a replacement of Hinduism by Buddhism, but rather a process of syncretization. Here I am curious about the "various theories" you note, which link religious transition the fall of Angkor? The religious flux during the late Angkorian period was not monodirectional (e.g., Hinduism losing power to an ascendant Buddhism). Instead, Cambodian elites began to patronize first Mahayana Buddhist institutions, before a period of Hindu reaction and repression of Buddhism, and then a turn towards Theravada Buddhism. The chaotic nature of (elite) religious life in the late empire seems to me to be the result of shifting institutional power given the empire's decline, as opposed to religious change shaping institutions.

Most important for this story, though, is the fact that contemporary Cambodian Buddhism retains a number of traits which resulted from a long period of syncretization with Cambodian Hinduism. The process was thus not one of replacement, but instead of coopting Hindu institutions. For example, Hindu-influenced rituals such as the Royal Plowing Ceremony form an important part of royal ritual legitimacy. The Ramayana is the backbone of Cambodian national drama and literature. And Hindu deities are still revered, albeit in different and diverse ways.

All of this is to say the process of transition from Hinduism to Buddhism in Cambodia was long and complicated. Cambodian Hinduism did not go away, but instead continues in various ways in Cambodian religious and cultural life.