I can't see much to make someone sick here- a language's rules are created by consensus among the speakers of the community, so if a form is widely used and understood by members then it has a degree of acceptability. This could be confined to regions or variants, etc, though I don't think this is the case here, but all that would mean is it is acceptable to a sub-division within the broader speech community. I would say that being used and understood by a speech community is a reasonable measure of acceptability.
I do not think they are mutually exclusive terms. 5jj's are examples of absolute clauses.
Quirk et al., p1120Nonfinite and verbless adverbial clauses that have an overt subject but are not introduced by a subordinator and are not the complement of a preposition are ABSOLUTE clauses, so termed because they are not explicitly bound to the matrix clause syntactically.
Absolute clauses may be -ing, -ed, or verbless clauses, but not infinitive clauses
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Quirk et al., 17.28Postmodification by nonfinite clauses
Postmodification by -ing participle clauses
17.28 Postmodification of the noun phrase is possible with all three of the nonfinite clause types: -ing participle, -ed participle, and infinitive clauses. The correspondence between -ing clauses and relative clauses is limited to those relative clauses in which the relative pronoun is subject:
will write
will be writing
The person who writes reports is my colleague. [1]
is writing
wrote
was writing
The person writing reports is my colleague. [1a]
The nonfinite clause "writing reports" in [1a] may be interpreted, according to the context, as equivalent to one of the more explicit versions in [1].
It must be emphasised that -ing forms in postmodifying clauses should not be seen as abbreviated progressive forms in relative clauses. Stative verbs (e.g. occur), for instance, which cannot have the progressive in the finite verb phrase, can appear in participial form.
This means:
The drunk driver is to blame for the traffic jam which was occuring yesterday.
and
The drunk driver is to blame for the traffic jam occuring yesterday.
=
The drunk driver is to blame for the traffic jam which occured yesterday.