Dukat was a narcissist, yes, but he, as you say, cannot outweigh simply arithmetic through his narcissism. I am strongly doubtful that Dukat wouldn't have had some clue as to the true strength of the Dominion; you do not simply "mislead" someone on such a matter. An appropriate analogy would be the United States trying to lie to the leader of an extraterritorial entity about its true size in order to let it be annexed into the Union. It doesn't really make sense.
You also seem to be taking a lot of leaps. A conquering army is not the same as an occupation army; the Dominion's large fleet of warships sent through the wormhole at the end of Sacrifice of Angels would've been mostly useless for controlling a domestic population. It is also clear that the Dominion does not
strictly rely on simple force to keep its empire together, and that it does
make extensive use of diplomacy to build complex alliances that help maintain the integrity of their union. Yes, the threat of force is always there in the background (but then again it is as well in the Federation, so it's a wash), and it is also clear that the Dominion is strongly authoritarian in nature, but it is also quite clear that they do not require large numbers of ships and troops absolutely everywhere at all times to keep the Dominion intact. There is no reason to suspect that the Dominion would've fallen apart domestically if they sent a substantial portion of their military forces to the Alpha Quadrant.
Little, if anything, in the episode proves that the Dominion is vastly more powerful than the Federation. There is more evidence, in my view, that shows the Dominion is not, though it is not conclusive either way.