The bird was stiff when you pulled it out because rigor was at its peak.
I'm not a worming expert as would be indicated by the fact that I almost never do it. But I have a couple questions.
Where would chickens get worms in the middle of winter with the ground covered with snow?
Some roundworms have a direct life cycle where the worm eggs are passed from the chicken and then in turn eaten by the same or another chicken. Other worms need an intermediate host like grasshoppers, crickets, beetles, flies, slugs, earthworms, etc.. I would think if the chickens were wormed when cold weather hits, they wouldn't need it again till things start coming to life outside.
Embryonation of nematode eggs in cold dry conditions can take a long time if at all.
To avoid direct cycle parasites, management that prevents chickens from picking in their own droppings or at least keeping feeders full will prevent a lot of that.
Are you concerned about using the same wormer so frequently? Parasites become resistant to the same anthelmintic after 8-10 generations.
I thought Piperazine had a withdrawal period of 7 days. Then perhaps another 3 days for the azole. Does that mean you can only use 2/3 of your eggs during the production season?
Have you done fecal float tests to determine if worms are present? I would think with your knowledge and skills you probably already have the equipment to do your own floats and examination. A microscope that magnifies from 100X-400X is sufficient.