They had a very easy way to reference the Dominion War in this episode. Picard: So Soji, as you can see online, I am a highly decorated former Starfleet officer who saved the galaxy multiple times and you can certainly trust me. Soji: You might not really be Picard. You could be a changeling. Picard (pokes finger): Do changelings bleed? Soji: Actually, they found a way around that too, the changeling impersonating Chancellor Martok bled. Picard:
Missed opportunity, as Odo is practically Deannas uncle! (Just kidding, he would make no sense on this show, plus R.I.P. Mr. Auberjonois.)
The gist of the "Bad Guys" plan in that movie was that they were going to steal the curative powers from the planet. Admiral Doughty's plan would not have worked even if he had been paying attention.
Bashir thought about using Odo's substance to make organs for transplantations. You know you'd have a glass of goo and you could tell it to take the shape of a heart or a lung...
I wonder what kind of The Lord of the Rings style epic that Thad would have eventually written about his Middle-Earth?
That cake is going to come back into play very soon. Now that Agnes is in a coma, Rios is going to question Raffi about what she put in the cake. As far as he knows Agnes threw it up and then went into a coma.
Well he certainly would have pointed out that Elnor's name means Star Trek in Elvish (this actually is the case). And if he started inventing languages without first learning Klingon, well... that would just be funny.
Heck they don't even need to mention the Dominion War. It could be as simple as saying the Federation having experienced a galactic war in recent times. Keep it vague for the newbies. (Everyone can relate to how deliberating any war can be). And us trek experts would know they were referencing the Dominion war. Best of both worlds.