I KNOW it's old-fashioned, but this might help--if you're from the
old school that worries about pronoun reference, you'd say the "whiches"
in these examples are misused.  These "whiches" have no noun or pronoun to
refer back to--most handbooks call this usage "broad reference," and state that
"this," "that," "which," and "it" cannot refer back to complete
statements or ideas, but must refer to a single word.  The handbooks
usually suggest that such sentences be rewritten for the sake of
clarity.

Also, the "as" clauses can be moved not only to the opening of the
sentence but to the middle of the verb; the "which" sentences cannot.
That the "as" ones can be moved to the verb suggests very strongly that
they are adverb clauses.

P.S.
Could this "which" problem be related to the increasing number of "which"
fragments that I see in newspaper writing and even professional journals?