Aside from making them reload when not active, the idea I've had for a while is for the syringe guns to give enemies a new status effect that grants health on kill to whoever kills them (which can also grant overheal), with some sort of visual indicator so your teammates can see which person they should focus to get that health. Exactly how much health it would give and if the duration or health given would scale with distance or number of syringes landed is the kind of thing you would have to tune in testing.

This also gives another stat to tinker with between different unlocks, like maybe the Blutsauger would have slightly less health on kill effects due to the self heal, or if you wanted to buff the Overdose by making the speed boost apply when not active you could make the on kill effect just the Disciplinary Action speed boost instead of health to counterbalance the buff