You hit the nail on the head. Tifa was always my favorite character in the game, and examining and re-examining her lines through this translation process has only enhanced that, making that percieved "plot-hole" of her not telling the truth into a heartbreaking, and understandable, character flaw.
And you're very right, she does most probably believe Cloud became a Soldier, even if she knows he didnt come to Niblheim. Her complimenting Cloud in Gongaga is probably her trying to convince herself that "it's ok, I probably have it wrong, he was a Soldier after all, etc.", or maybe shes even trying to stop Cloud from remembering Zax if in fact he knew him, which would trigger his "going distant" (this whole scene happens after meeting Zax's parents).
I double-checked all this points you mentioned as well, Matski, and yep:
1) Tifa's reacts the same in Japanese, worry in the guise of a joke.
2) Dio says literally "I met Sephiroth recently" in the letter. just casually ya know.
3) Barret had never been to Cosmo Canyon, and Avalanche was initially formed by some dude who studied in Cosmo Canyon and then moved to Midgar. this is actually a plot point in Crisis Core i believe? but, we don't speak of that game.