I've been doing a bit of digging and it's looking like "spiritual sequel" is right, that this will be a Halloween III type situation, using the name to present a vaguely similar but unrelated story. Some people claiming to have seen an early screening back when it had a different working title basically spoiled the whole thing, and if what they say is true, the film doesn't involve the giant monster scenario from Cloverfield at all.
Ah well. I'll still be getting those new Godzilla and Gamera movies sometime this year, and this movie does look good despite how much or how little it has to do with Cloverfield.