I stand on the hens only need bred once point....
From Pa Game commission site: When do turkeys in PA breed, nest and hatch? Breeding can begin as early as the end of March, when winter flocks disperse. This is the time when hens seek a nesting area and gobblers begin gobbling in earnest. A hen can be bred by the gobbler daily, but the sperm is held in the hen's oviduct for up to four weeks. One successful breeding is sufficient to fertilize the eggs for an entire clutch (sometimes two clutches, if the hen loses her first nest and successively re-nests).
There are other references, but this one was easy to find.
Where did you get 4,000 -6,000 hens killed? here is a link to Ky harvest for fall 2017
http://app.fw.ky.gov/harvest/turkeyharvest.asp Male Female Total % Male % Female Adult Sub-Adult Archery Firearm Muzzleloader Crossbow
Total 705 1193 1898 37.1% 62.9% 545 160 645 1007 2 244
Here also is a link to the study that explains the reason for the survey and population trends
https://fw.ky.gov/Hunt/Documents/2018_KY_Turkey_Report_Pre-Season.pdfSo a total of 1898 turkeys were killed during fall of 2017 of which 1193 were hens. with a population of approx 350,000 turkeys .54 % or 1/2 of 1 percent of the population was harvested....that in my book is statically inconsequential