Problem is the poults aren't being born cause they are never conceived, deer can and do breed at night without hunter interference ,but turkeys are up in trees at night, they live a daylight till dark existence where deer are 24/7 doing their thing. If you think about it, every time a gobbler opens his mouth within earshot, somebody with a gun is after him, disrupting the breeding process. It's not universal, every single instance of breeding isn't disrupted but if enough is, if you have X amount of barren hens because of it that would otherwise have been bred, you've got a falling population. I've seen far more barren hens in the summer now than I ever did before.
Maybe instead of closing the season, just don't have a spring season and only a one gobbler fall season for 2 years as a trial?