The inability to build starships to meet the demand, any demand, is built into the very structure of Trek drama. Otherwise how could Starfleet always be so starved of ships that the heroes arrive at or after the nick of time, when just adding a thousand ships would make the colonies safe?
They don't need sleep or food
To be accurate, we don't really know that. We know the White keeps them going, possibly for days at an end, and we know they refuse to sleep or eat during a mission. But they do have digestive systems, and they do seek and consume food in "Hippocratic Oath".
In "To The Death" Dax suggest to a Jem Hadar to get some sleep, and he replies they don't sleep, and don't eat either.
It's the White that's most likely responsible for it, but then again, they're also genetically engineered too (the sleep part).
I can easily see these guys as the ones building the ships really fast for the Dominion.
Seems like DS9 wanted to establish that the Federation couldn't keep up with the Dominion--for dramatic effect.
In that case you can see the difference with the Klingons ...they were fighting longer than anyone, and yet by the time of the Dominion war they still had enough fleets of ships to fight the Dominion.
I think the Klingons believed in stockpiling huge amounts of ships, so they were able to last through the Cardassian war, then the Federation war, then the pre Dominion war.
However they got worn down by the time the war actually started.