It's like with this old saying about how You eat an elephant (a piece at a time). Same here - this can be done slowly and gradually. It does not have to be done out right.
They could start with limiting current sale of guns (by bringing some control over to who can buy what and when). Introduce some sort licences (but maybe for guns bought after the law was introduced). And than taxing the shit out of bullets (for personal use). Prohibit trade of guns between people (only b2c, this could be quite hard and unpopular but could address the problem of existing guns). And then start to buy guns of people with sufficient premium on price.
This could be costly but I believe that over the time would eliminate this strange culture of mass gun possession.
