When we recall dreams that take place in the subconscious during sleep, is that a part of the mind still above this deep level of the subconscious that is cut off and inaccessible to the conscious self?

They can, in some instances, reflect what is going on in the deep subconscious, but will most likely be somewhat above that level. And that is why a connection to them is occurring and a conscious recollection of what was being experienced will often be retained in memory, or at least for a short while, and may slip away if the person does not care to retain the information, or if they go back to sleep it may slip away because there is not an opportunity to consolidate the memory by holding onto it for sufficient length of time for that to commence. So it may be something remembered for a few moments, but then gets lost again. This is a common occurrence on waking and remembering a dream in progress. But if sleep is allowed to come back, on reawakening they will probably not recall the dream sequence itself.