Unless heads get dimpled or just won't hold tune they are fine for quite a while. If the kit is played hours and hours a day heads may only last 3 weeks, if it is played an hour a day every couple of days then heads could last a year.
There is a huge difference between batter and resonant heads. Resonants are not designed to be struck so they will dimple or rip easy, not to mention that if you were to use a resonants on both sides of a drum it would most likely ring very badly.
The key to controlling overtone is the batter head used and adding additional dampening if the head does not remove enough ring to suit you, along with tuning.
Sounds like you need new batters on your toms anyway, so I would start there with 2 ply heads (Evans EC2s or
Aquarian Performance 2). These heads have built in dampening and most of the time that should be enough to fix the problem. If not Moon Gel or dampening rings can be added to further control the overtone.