I'd like to join the conversation, though a little late.
As this is my first post to this dicussion (other than regarding preliminary matters), I'll mention first what I have said in another thread some time ago, that my Greek education was through a classics department; I did some linguistics but wouldn't consider it more than a nod to the field, so I'd be pleased to be corrected wherever my thinking and terminology goes astray.
My initial impressions on R's first section are that I like the simplicity of his approach, not being concerned with the morphology but with the semantics of the different stems. I do not subscribe to the view that Greek does not grammaticalize tense in the indicative, so I am on-side with him in that.
I am inclined to doubt his claim that the aorist stem denotes a completed action. I regard the aorist as [+completeness] but neutral as regards completion. It's been expressed before, perhaps on B-Greek, but it's true that it's easiest to think of completeness and completion together; but it is possible to view even an incomplete action beginning in the past 'globally' (i.e. in its completeness) without regard to internal processes. There are sufficient instances of aorists used where the action is not completed for me to regard this as uncontroversial; in this connection I mention Smith's 'Errant Aorist Interpreters' not because its treatment of the aorist is excellent beyond others, but it is worth reading and available online (http://faculty.gordon.edu/hu/bi/Ted_Hildebrandt/New_Testament_Greek/Text/Smith-Aorist-GTJ.pdf
The 'he began to reign' type of examples also call into question a claim for completedness, as it seems to me special pleading - since they are not formally distinct - to say of these that they are explained by the beginning of their action being completed, so I look forward to R's account of these.
Another matter that this first section raises in my mind is the matter of semantic value and pragmatic implicature. I'm quite happy with the idea that "completed" is a frequent part of the pragmatic implicature of the aorist in the indicative, but I'm not convinced of this as invariable. So, what is the current consensus - if there is one - regarding the question of 'cancelability'? My understanding is that some writers raise to the status of semantic value only those meanings which are present in all instances, without exception, while others do not set so uncompromising a standard.
I'll also be interested in R's treatment of those aorist participles that clearly do not denote an action antecedent to that of the main verb.
Finally, the meaning he attaches to the word "aspect" is not how I think of it; I take aspect to refer to the way an action is presented, either in its entirety or with regard to its internal process. Campbell (Verbal Aspect...
, 2007) begins, "Verbal aspect refers to the manner in which verbs are used to view an action or state. An author/speaker will portray an event either from the inside, as though it is seen as unfolding, or from the outside, as though it is seen as a whole." The meaning R ascribes to aspect seems, from what I have read, closer to what I had thought Aktionsart was used to describe.
So, having declared my ignorance and some of my starting assumptions, I'll be interested to see the unfolding of R's views.