More on sentence adverbs

While thinking about the "hopefully" debate in another thread I
noticed something rather odd. As noted there by Eric Walker and
others, normally it's possible to transform "it is X that..." into the
sentence adverb "Xly", e.g. "it is possible that he will arrive
tomorrow" can be rendered as "possibly he will arrive tomorrow" or "he
will possibly arrive tomorrow" with little or no change in meaning.
The only systematic exception I'm aware of is when X has negative
effect; we can't turn "it is impossible that he will arrive tomorrow"
into "impossibly he will arrive tomorrow".

But the pattern breaks down when X is a passive participle. We can
say, for example:

Reportedly there has been a disturbance (= "it is reported that...")
Admittedly there may be unforeseen problems (= "it is admitted
that...")

but not:

Expectedly he will arrive tomorrow.
Believedly there has been a disturbance.
Fearedly there may be unforeseen problems.

even though the corresponding sentences with "it is expected/believed/
feared that..." are unexceptionable. Why not?
.