What I am learning in channeling the subconscious mind is that it bypasses some resistance caused by beliefs embraced by the conscious self. Do these two levels of the mind each have a compartmentalized store of beliefs independent of one another?

It is not that they have a different compartmentalization, it is that there is a difference in how they utilize beliefs. Each has power, each has consciousness, and has independence in the thoughts. It is the case that both draw on a common set of beliefs, but those in conscious awareness can simply be more robustly reinforced by the conscious part of the mind, and as a result, it is the conscious part of the mind that must become convinced that the beliefs can be surrendered and replaced, and this may not be easy to do. As a result, a belief replacement arranged through the subconscious may not be fully implemented if the conscious mind is unwilling to let go, or the belief may simply be re-created through simple memory of having its existence in awareness and assuming that this is still the case. Beliefs can be re-instilled this way quite readily as the mind is restless and always wanting to learn and grow, and sometimes it simply expands its own follies and limitations to deepen and worsen them. The main problem is that many beliefs are beyond reach, and these include many of the deepest and darkest. So there is much to be done to rescue people from this dilemma.