I tend not to put much stock in the novels, as they frequently conflict with each other on pretty major things. For instance, one has DS9 destroyed, one doesn't... hard to enjoy so many random inconsistencies like that.
What? That may have been true in the 90s, but since 2000 or so Pocket Books has worked to create one cohesive novel continuity which actually works out better than some other shared universes, arguably better than on-screen Trek. At the very least, you're wrong about the destruction of DS9, that's been a major event that all the novels have stayed consistent with. It's true, since the novel chronicling its destruction was published there have been a few with flashbacks that take place on the old station prior to its destruction, but that is an inconsistency at all. That's like saying Cause and Effect is inconsistent just because the crew of the Bozeman are wearing TOS movie uniforms.
What are all these references? I only know of Picard's one remark.
The five onscreen references to Starfleet not being military:
-Picard in Peak Performance
-Archer and Admiral Forrest in The Expanse
-Archer and Captain Hernandez in Home
-Scotty in STID
-Scotty in Beyond
Of course, of these five two are about the Starfleet that existed before the Federation, and two are an alternate timeline. Peak Performance remains the only on screen reference to the Prime Universe's Federation Starfleet being non-military, despite the fact that it had been described as a military a year earlier in Hide and Q. Peak Performance is also the only reference to Starfleet being non-military prior to 2003.
Now you're breaking your own rules. You said earlier you don't count novels, therefore you can't reference one written by Nichelle Nichols. No it doesn't matter that you were referring to fictional works and Nichols' is non-fiction. A novel is a novel, you can't cite one immediately after saying you don't count them.
Besides, Shatner's novels do describe Starfleet as military.
Or that they used federation credits. The only credits i ever heard was transporter credits and that was clearly self explanatory.
The Trouble with Tribbles, Cyrano Jones and the bartender are haggling a price in monetary units.
Farpoint, Dr. Crusher says "charge it to my account."
Starfleet is essentially nasa with weapons training.
Then why does Starfleet follow the military tradition of referring to COs as "Captain" regardless their actual rank, and not the NASA tradition of referring to a CO as "Commander" despite their actual rank or title. Why isn't the head of Starfleet a Director if they're NASA? If anything those guys in the gray jumpsuits scene frequently on TNG seem more like a NASA analogue to me than Starfleet ever did.
