Swimgirl, Twin Peaks' carb cycle is one thing, but I don't think what you're trying to do is the same thing. It appears to be more of a structured calorie cycle, along the lines of say Aceto or Venuto. In which case, I wouldn't mix in TP's stuff if I were you.
I found fruit to be a big fat (and I mean that) no for me when trying to shed weight. (Which is one, though only one, reason why I suspect TP's plan -- sorry, TP -- was so very, very wrong for me). And dairy doesn't "cut" it for me either, so to speak. (Nor for a lot of other people. It tends to make one hold water weight, for one thing, which while not exactly fat, is discouraging. For another, the carbs in dairy are sugar carbs -- lactose -- which of course in any significant quantity can cause fat loss problems if you are at all sugar-sensitive.)
As for the two meals being no-carb -- again, that's TP's plan specifically. And if you read the plan, you'll see why: there is no limit on carbs on the high-carb day. If all your meals of six meals are no limit of carbs, with carbs -- well, if you have any Carb Capacity at all, you can easily see how one could well pack away far too much without the safety factor of a couple no carb meals.
On bagels -- less the GI factor than the lack-of-nutrients factor. You'd be better off, specially if you are restricting cals in general, to go with something that has a little more to offer. Beans. Whole grains. Sweet potatoes. With restricted calories, one's nutrition tends to suffer anyhow (especially if one is a female, since even on a typical female maintenance diet of around 2000 calories, it's apparently darn near impossible to stuff in the RDI of all requisite nutrients) so you basically don't want to waste a significant fraction of your day's allotment (one bagel, 200-300 calories at least) on something that isn't giving you full bang for your caloric buck.
Now, on your calorie division. If you are doing structured calorie cycling, here is what you essentially want to accomplish: an overall caloric deficit, weekly, with a rotation of calories, daily. Does that make sense? So if, say, your maintenance is round 1900 cals, and you eat 1200 cals for three days, and then back to maintenance every fourth day, you are averaging either 1300 or 1400 cals per diem for that week. Which is a total deficit of either 4200 or 3500 calories per week -- only you are varying it constantly as you can see, not only every few days but even weekly, so your body never gets accustomed to a drastically lowered feedbag.
That help?