That's a good point, the "break up your move" specifies "more than one weapon attack".
Which gives us some indication that the eldritch blast attacks are more closely-spaced than weapon attacks. So I think we have several degrees of "how tightly spaced are these attacks":
* Magic missile: Simultaneous. Nothing can happen "between" them.
* Weapon attack: Sequential. You can see the results of each before choosing what to do next. You can use part of your move between them. A reaction triggered by one attack can take effect before the next attack.
Now, there's three things we've established can happen between weapon attacks. There's "re-evaluate situation and make new choice", there's "use part of your move", and there's "reaction triggered by one fires before next". And it sounds like, intuitively, most of the posters here agree that eldritch blast does allow "re-evaluate situation", does not allow "use part of your move", and may or may not allow "a reaction can take place before the next one happens".
So I think one question worth asking would just be each of those as separate questions. Another would be whether those have some kind of innate ordering. For instance, a possible rule (which I don't think I've seen anywhere) would be that basically attacks have a Timing Class, of some sort. Simultaneous is the fastest, and denies all three. Nigh-Simultaneous could allow new choices, but not reactions or moves. Sorta-Fast could allow new choices or reactions, but not moves, and Weapon Speed would allow new choices, reactions, or moves to separate events.
And in this theory, then, anything which allowed moving between events would necessarily allow reactions and new choices, and something which allowed reactions would necessarily allow new choices, but might not allow moving. So they require different amounts of time, but if you have enough time for something, you also necessarily have enough time for anything that's faster.
Until I hear otherwise, though, my ruling will be:
* Anything that has "attacks" allows you to make new choices between "attacks".
* Also, anything that has "attacks" allows reactions to occur between them.
* Only weapon attacks allow movement between attacks.
* Things that do not have "attacks", such as spells where you designate multiple targets and they make saves, are simultaneous unless stated otherwise.
* Magic missile says "simultaneous" because it's enough like attacks that some people are likely to think it counts, even though there's no to-hit roll, and/or because this question used to exist (say, in early 4e) and the devs are being careful to clarify the wording.