[I sent this from the wrong address so it got bounced, sorry]
Strike the "valid but unspecified" definition. Stop using it.
Up-front in the "method of description" front matter, state some things about standard library types:
"Types defined in the standard library describe preconditions on their
functions and operations. Those functions can be used whenever preconditions
hold (implying functions without preconditions can always be called). These
guarantees hold during the object's entire lifetime (including after the
object has been moved from)."
This reinforces [basic.life]. Of course the object meets its invariants (whatever that means) so let's not say that, it is tautological. Now we never need to say "the object is in a valid but unspecified" state in the specification of standard library types. It's just a truism that they are always valid.
"For program-defined types the standard library does not require that
objects have a state where all supported operations are still allowed to be used.
[Note: this follows from the fact that the library cannot know a
program-defined type's preconditions on its operations.]
The operations required on a type by standard library components
are explicitly specified, and (except for equality preserving operations) are only performed on the values provided as arguments [Note: For example, such operations are not performed on values created after an object has been moved, unless specified otherwise.]"
We might then need to make it very clear that assignment and swap are required to work for any value, including moved-from.