Culling females is and always has been the key to population numbers the culling of males will have little if any effectIME it's best to do like awmc suggests, clatter the females hard every year, right from the start, the females always seem to be naturally more cautious than the males of many if not all the species, and the males are overexploited in many areas.
Shooting males in the female season is simply wasting time, and effort.
Proper forest design helps to get to grips with essentially a man made problem.
If every stalker in the country shot 4 females in order to obtain licence to take one male, it would be a start.
Putting run winter stags into the food chain does nothing for the marketing of venison as a quality product, that'll take the shine off the venison cheque for everyone, same with later/OOS hinds. Bean counters make these judgements, not deer managers, they probably think venison means 'sausages' or 'burgers', not something of real quality or value.
on overall numbers , but over culling of males will have a negative effect on the age range of males.