SZ, section 65, H. 329

From the very outset, your post clearly said:

"Blattner differs in that he (A) points out the thesis which he believes to be pivotal to Heidegger whole magnum opus, and (B) puts this thesis into question, actually claiming that Heidegger fails to demonstrate it."

So there seem to be a few questions that need to be addressed to get us back on track:

1) Is this something that requires demonstration?
2) If so, does H. ever attempt to explicitly demonstrate this? (Does Bl. mean by "failure to demonstrate" that H. never attempts to show this or that his demonstration fails?)
3) If H. has attempted to demonstrate this point, where does he do so? (What sections of SZ, etc.?)
4) If he does not, can the rest of his work serve as an implicit demonstration?
5) Does the demonstration (if it exists) really fail?

Also:
6) Is this thesis that important to H's project?

How does sequential time arrive out of non-sequential time?
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As a brief and preliminary response--here is what I believe to be a key passage (H. 329):

Das Charakteristische der dem vulgären Verständnis zugänglichen »Zeit« besteht u. a. gerade darin, daß in ihr als einer puren, anfangs- und endlosen Jetzt-folge der ekstatische Charakter der ursprünglichen Zeitlichkeit nivelliert ist. Diese Nivellierung selbst gründet aber ihrem existenzialen Sinne nach in einer bestimmten möglichen Zeitigung, gemäß der die Zeitlichkeit als uneigentliche die genannte »Zeit« zeitigt. Wenn daher die der Verständigkeit des Daseins zugängliche »Zeit« als nicht ursprünglich und vielmehr entspringend aus der eigentlichen Zeitlichkeit nachgewiesen wird, dann rechtfertigt sich gemäß dem Satze, a potiori fit denominatio, die Benennung der jetzt freigelegten Zeitlichkeit als ursprüngliche Zeit.
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A couple of issues:

1) Concerning "the time accessible to our ordinary understanding"...isn't this world time? It doesn't make sense that our ordinary conception of time is what is accessible to our ordinary conception/understanding. Rather, the conception is derivitive from something else which is accessible to it.

We may not agree on this point. Even so, from now on when I refer to ordinary time, unless specified otherwise, I mean either world time OR our ordinary conception of time since it isn't clear to me which one is being spoken about here.

2) Isn't the key characteristic of ordinary time "that in it (ordinary time), the ecstatical character of original time is leveled off? "As a beginning-less and endless now-series" seems to be qualifying the main point.

H. then says that on the condition that he shows ordinary time to be derivative, he is justified in calling the temporality he has exposed to us 'original time'. (This seems a bit tautological, doesn't it?)

3) The demonstration, then, involves showing that ordinary time is not its own foundation. While sequentiality is one of the characteristics of this kind of time, it is not this aspect that needs to be demonstrated. We simply want to see its derivational character.

On the other hand...
how would we ever get to know what the origin of ordinary time is? According to H., there is something we already know about it: Original time reveals something about itself in ordinary time; original time shows itself to be that which is covered over by ordinary time. (this is after all the main characteristic of ordinary time).

So, now what needs to be demonstrated is that ordinary time:
A) is grounded in something else
B) covers over its ground (since the only way to demonstrate A is to expose the ground and the only way the ground can be exposed is as something hidden by ordinary time.

Point B is precisely where the series of nows comes in to play since it is as this that ordinary time covers over its ground and thus that original time shows itself (and thus that we can see that ordinary time is derivative and not original time. And thus that we are justified in calling original time 'original time')

H's point seems a bit circular (surprise!). So the question is: Can this be demonstrated? If we delve deeper into the hermeneutic circle, will we find a richer "demonstration"? How does the series of nows "level off" original time? Is it simply because the latter is non-sequential that the sequentiality of ordinary time covers it over? Or is it for another reason? H. is not clear about this. Maybe this is self-explanatory, but in that case, I have other questions.
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"H. then says that on the condition that he shows ordinary time to be derivative, he is justified in calling the temporality he has exposed to us 'original time'. (This seems a bit tautological, doesn't it?)"--
It does, indeed, if one assumes that "the key characteristic of ordinary time is 'that in it (ordinary time), the ecstatical character of original time is leveled off'."
For, if this is the way H. defines "ordinary time" (and what else can "the key characteristic" be if not a defining one?), then he has no need to "show" (or, to use even more accurate translation of the verb nachweisen--to demonstrate) the derivative character of the ordinary time; such a character being presupposed in the very definition of the latter.
This is precisely why I strongly disagree with your reading of this phrase. I believe that H. here defines "ordinary time" as "a beginning-less and endless now-series".
I.e., the key characteristic of it is its being an endless and beginning-less sequence, every element of which is a now.
This is an immediately recognizable (epi-)phenomenon. I.e., H. begins with an "appearance". What remains to be demonstrated (or, proven) is that this is only an appearance; or, in other words, that this phenomenon is derivative.
Demonstrating this is precisely the task H. sets here for the rest of the book.
Only having fulfilled this task, H. will have the right to call "temporality", which he first introduced earlier in the same section (H. 326), "originary time." For, to have a right to call anything "originary" (ursprünglich), one has to show that something does originate (entspringt) from it.
At this point (=in section 65) H. does not yet have any grounds for claiming the existence (or Zeitigung, or whatever) of originary time. He thus could not possibly introduce here ordinary time as an originary one leveled off.
I infer from this that H. here says that in ordinary time "the ecstatical character of originary time is leveled off" only in anticipation of the point in his exposition at which the originary character of--i.e., the derivation of ordinary time (defined here as an infinite sequence of nows) from--temporality, will have been demonstrated.