evholten,
Is it possible that you are reading too much into the various terms here? I cannot know what Dvid Allen meant when he wrote them, but I do know that any writer or teacher faces the dilemma of either being too imprecise (few words, few steps etc and thereby appearing to lack clarity) or using too many fine distinctions (many terms etc, thereby appearing to be rigid and over-prescriptive) - and it is all perhaps just a difference in wording.
The way I see it is this: processing, reflecting, reviewing, clarifying, organizing can probably be seen a slight different kinds of mental activity, but tend to often happen simultaneously. Each time you do what you need to do, or want to do, no matter which of these facets happen to be most "lacking". For example, you read a note, reflect on it and clarify it as an clear enough action and put it (organize) on the right list, right project etc. As simple as that. And you probably do that whenever you see a need to, which is when you notice something that is wrong, incomprehensible, incomplete etc.
For me personally, I do not see any reason to schedule this to any particular time of day, or day of the week. It is an ongoing process (for me). For example, whenever I feel uncertain or curious about what is hiding in a particular project, I just take a look, and if I see something wrong I fix it right there and then (if I had not had the time and inclination I probably would not even have looked in at that particular time.). Or when I see an action that I do not understand I try to rethink it and rephrase it.
In addition I do my weekly reviews (and more thorough reviews a few times a year, and very quick daily reviews) just to check that everything is OK and fix anything that I had missed during my more spontaneous reviews. I find that useful, too, because I otherwise tend to leave boring stuff to the wayside. The daily review also serves as a tentative "day planning", identifying a few actions that seem to fit in with any calendar actions or other known factors, such as weather, visitors in town, whatever...