Dukat didn't really care about arithmetic/feasibility when it came to his narcissism.
Christopher's example with the bajorans proves this.
It was made clear in 'The search' that the ONLY think keeping conquered species in line is the threat of the jem'hadar. NOT diplomacy, nor anything else.
The founders are FAR too paranoid to allow themselves to become vulnerable to domestic revolt for a foreign adventure.
Meaning, the massive dominion occupation army (needed for a massive territory) was in the gamma quadrant.
So was the main dominion industrial base.
The dominion expeditionary force and its rushedly installed industrial base was close to overwhelming the federation+klingons and kept up with the federation+klingons+romulans.
If an expeditionary force could do that, then the dominion, in its entirety, is FAR stronger than the federation+klingons+romulans.
The ease with which the dominion created jem'hadar (and ships) leads to the same conclusion.
As does the age of the dominion - 2000 years spent conquering.
On the other hand, there is little evidence that the dominion is weaker than the alpha quadrant powers - of course, you named none.