The problem with crossing over the two stories isn't in the present, but in
the way they put different spins on the same past; and there's only one past
for both stories, since that past is the series.  You can't resolve these
two incompatible pasts.

The best you _can_ do is probably what you did: have characters think about
things from their point of view, without authorially saying that a particular
viewpoint is correct.  Lots of fiction limits itself to character viewpoints
anyway, so this device easily slides by the reader.

But in this case it's cheating.  You're saying "it might or might not have
happened this way"...  but you're dealing with two stories, and in the context
of each story it _did_ happen that way.  Instead of picking one story to
believe and casting doubt on the other, you're dividing the doubt equally
between the two, and that really doesn't work any better.