As the Exterminator from last game, I can vouch for how much the odds are stacked against the role. You're essentially trying to night-kill every townie without the support network that the dopples have, AND every dopple without the trust of the town.
The role is essentially a Team unto itself, and to win you'd have to be extremely tricky and extremely lucky. Perhaps combining them with the concept of the Mad Scientist you had would help balance them out.
Along with their power to night-kill, give them a selection of "gear" to pick at the start (1-2 of the following):
a one-time-use Personal Shield (which would work once as though guarded by the Protector)
a one-time-use Holoform Modulator (which would work once when investigated, allowing you to choose a role to show as)
a one-time-use Scanner (which would work once as the Agent)
Depending on your feelings about the individual powers, some may be able to be used more than once. The Exterminator could then effectively operate Solo, lurking and working in silence, or could privately ally with the Town (providing a fairly powerful, but dangerous mercenary aid against the Dopples) or the Dopples (providing a second kill, an armored target, and a limited-use investigator). Of course, both sides would know that any alliance would only be temporary, and an offer of protection from the other party may sway them to betrayal.
On the subject of what happened with the crossed night-kills, I think they should execute simultaneously rather than in an order of operations. If two killers target each other, both die. If one killer targets a player, and a second killer targets the first, then the target should die, and the first killer should die.