I think I can see the underlying thought-processes here, anox (I have been known to be wrong). Prepositional phrases have varied roles.
Contrast (all examples from the Internet):
1. New Dumbo ride ...has opened with surprising details and eye-pleasing features.
Here, the PP really gives extra information about the new ride rather than the opening process. This is seen by restructuring (though this does give a slightly different emphasis):
New Dumbo ride ..., with surprising details and eye-pleasing features, has opened.
If I had to, I'd class your first example as being of this usage, though it feels a little clumsy to me. I'd prefer:
The story leaps back and forth in time. Scenes set in disparate places are crisply juxtaposed.
2. [T]he door opened with surprising ease for its apparent weight.
In this case, the PP is adverbial, describing the ease of performing the action. Your (second sentence) example is of this class, if rather longer. Try substituting seamlessly for with ... channels.
3. The film opened with a lengthy introduction to May as a child.
Arguably, opened with should be regarded as a multi-word verb here (there isn't a one-word replacement, but included is in the same ballpark).