Sounds like an interesting structure, one which may confuse the hell out of people (it already confuses me lol). I would say it would probably be better to have it in a sort of Haruhi Suzumiya no Yuutsu kind of structure, since it has worked so well. I really would think Haruhi would just be an run of the mill, ordinary type of anime if it were aired chronologically, and not mixed up. One does have to admit that it was genius to market it that way though.
I'm not sure how you'll be presenting the climaxes, but I'd suggest having the one in the first chapter be as a sort of hook, one that reveals the end, but in a brief sort of way, with the climax at the end as the actual climax, that goes over the content of the first one and but presenting it in an omniscient view, that reveals something crucial.
With the body of the story, it might work to have bits of the "introduction" nearer to the end of the story, or at least every so often throughout it. And perhaps have a bit of information leaking before the first climax (did that sound ambiguous to you? I feel like I should twist that =p), just to draw in the audience a little more.
Anyway, whatever you decide, I hope it works out. Post it some time and let us read it, yeah?