Remove the Genetics job and

[salix_catus]

If a medic is doing their job right there isn't supposed to BE any dead people. If you want to help people get better at keeping them alive. Medics exist for the living, let genetics handle the dead. Letting medics use the cloner just gives them yet another reason not to patrol the station looking for people to heal or drag back to genetics.

gah there is so much not right about what you are saying.
Doctors DO help people lots. you get the sorts that stay in medbay and help people who come to them dying. then you get the paramedic sorts that patrol the station with healthgoggles, looking for injured people and responding to calls for help. but they can't help people who get silently killed off on they're own or shot up to death in seconds. antags generally kill people without an audience. doctors can then only drag bodies to genetics and hope that the geneticists actually want to help or are actually even there and not hiding away with a portagene.
In space station 13 gibbing is the only real death. clinical death has just become another ailment to be cured with cloning. Giving the cloning procedure to the doctors makes so much more sense.

Also medical is such a big department that you might as well be making the cloner public at that stage.

Here. doctors and geneticists have access, yet cloning is still as closed to the public as before.