I built a syntax query to search for what Cascadia construed to be adjectival modifiers of NPs, where the modifiers were participial clauses. It yielded 376 hits (see attached image for the query). What was interesting is that a good many of these in the Gospels occurred at the introduction of a new referent, as in the two cases above. I can't think of a viable adjective the writer could have chosen instead of the participial clause, and I would consider this good Greek. Rather, the alternative formulation likely would have required the writer to have used two separate clauses to have conveyed the same information conveyed using the participial modifier. So in this case what might be construed as an upshift from a structural standpoint (adjective to clause) may functionally be more of a downshift motivated by elegance or economy (independent clause or relative clause to participial modifier). I attached a PDF with the rest of the results. They are illustrative; some participles I'd take as adverbial but the data still serves a purpose.Matthew 13:44–45 (SBLGNT) Ὁμοία ἐστὶν ἡ βασιλεία τῶν οὐρανῶν θησαυρῷ κεκρυμμένῳ ἐν τῷ ἀγρῷ, ὃν εὑρὼν ἄνθρωπος ἔκρυψεν, καὶ ἀπὸ τῆς χαρᾶς αὐτοῦ ὑπάγει καὶ πωλεῖ πάντα ὅσα ἔχει καὶ ἀγοράζει τὸν ἀγρὸν ἐκεῖνον.
45 Πάλιν ὁμοία ἐστὶν ἡ βασιλεία τῶν οὐρανῶν ἀνθρώπῳ ἐμπόρῳ ζητοῦντι καλοὺς μαργαρίτας·
The notion of rank-shifting is useful in that it describes what is happening from a structural standpoint, but it requires additional consideration along the lines of Levinsohn's "default/marked" and "choice implying meaning" principles to nail down more precisely the exact nature of the choice. Otherwise one is simply tallying structural shifts that don't mean much on their own. I know this is not what you have done or are advocating, Kimmo, your many posts here over the years make this clear.
I'd suggest taking more of a compositional approach to the problem. I claimed in a recent paper on the article that use of an attributive structure other than first position results in a change in the information packaging in the NP. Whereas first attributives result in essentially one package, the addition of the unneeded article in second and third attributives creates a second package. Looking at the distribution of third attributives, none of the ones in the GNT were restrictive. All conveyed non-restrictie thematic information that reshaped the reader's perspective of the referent. This use of third attributive instead of first would fall outside the bounds of rank-shifting, yet would seem to overlap with the kind of phenomena you're interested in accounting for from a pragmatic standpoint. Hope this helps.