SNW made Trelane a Q for the same reason that they had a holodeck episode. Because they want to make SNW into the next TNG despite the conceit of it being a prequel to TOS.
I agree that the episode's problem was being over-referential, but it's because of their (or more likely Akiva Goldsman's) desire to remake TOS, not TNG. "Blues" failed as an episode because its climax was just a rehash of "The Squire of Gothos"'s climax, which wasn't a good ending even in the original episode because it was a
deus ex machina where Kirk did nothing to bring about the outcome, beyond avoiding getting killed by Trelane long enough for the situation to resolve itself. It's not bad to revisit old continuity if you do something that adds to it or reveals it in a new light, but this was just pure nostalgia, rehashing a story we'd already seen, and it carried little meaning for viewers unfamiliar with the reference. Note how the only things we discuss about the episode are its TOS references, rather than its own story or character beats. The referentiality was the point of the story, so the story was empty in its own right.
I really don't see what SNW has supposedly done to make it "the next TNG." It hasn't done a Borg episode or a Ferengi episode. It hasn't shown first contact with the Betazoids or Bolians. Aside from doing a holodeck episode and casting John deLancie to deliver a couple of lines as a familiar-sounding but anonymous character, its references have mostly been to TOS-era stuff -- Vulcans, Gorn, Klingons, Robert April, Sybok, Rigel VII, and of course Kirk and the
Farragut. "Tomorrow and Tomorrow and Tomorrow" implicitly referenced ENT's Temporal Cold War and brought in the Department of Temporal Investigations from DS9, but was mostly referencing Khan and the Romulans. "Those Old Scientists" crossed over with
Lower Decks. The Illyrians are partly an ENT reference and partly a TOS/TAS reference, since D.C. Fontana's novel
Vulcan's Glory established Number One as an Ilyrian, one L, which may have been meant to be the same species to whom Harry Mudd sold Starfleet Academy according to TAS: "Mudd's Passion." And of course it's also followed up on the Klingon War from DSC. So it's referenced other series a lot more than it's referenced TNG.