That won't change a thing though as shown. People didn't learn after being banned for 6 months so why would reducing it to 3 months help? In 3 months you got the same hackers back into the game and nothing will have changed.
I've seen you people refer to some of the hackers I'm thinking of in this thread. They were all banned during the time we had a 6 month ban and they served their time but they always hacked again. They've been banned 2-5 times now and even if we decided to ban them for even a longer time, say a year, they still came back with hacks. As a GM nowadays I would be frustrated af if I banned a bunch of people and then I have to deal with them again in 3 months or less. To me it would feel like watching all those replays and analyze them, stalking the player in-game, talk with the right people, would all be for nothing.