You know, I wonder if it occurred to anyone that, instead of changing the role, we should instead be changing the strategy. Namely, dopps should learn to not PM during the day, since they may be seen by the watcher. A town base should not PM during the day, as they may be seen by a dopp watcher. I don't see why the role is so gamebreaking when it can be avoided by simply not PM'ing during the day. It merely means that extra precautions need to be taken. I'm personally for the "make it a 1-shot ability." You get the danger in the act without the realization of the danger all the time.
I was pondering this until I realized that it basically tears apart one of the inherent features that the dopps have: being able to talk to each other. Yes, they still get to discuss things at night, but much of the planning and organizing they have happens during the day, especially in vote manipulation. By making the Watcher even an option, you've stolen that away from them in every game (since you never know if one's around).
I'm all for the town having to worry about their PMs (or evil with it by slipping in fake PMs). Reducing Dopp chat to Night Only (or risking the entire game completely) is WAY too drastic for a roll that's meant to keep things interesting.
On the matter of it being an alien power.. so long as it's Exterminator only, I love it. It will let them find the dopps easily, but Exterminators can't spit out their info without losing (like the town will let them live). Besides, living dopps means more kills, so it's more useful to keep them around so long as they aren't targeting him. It can stay on rather than be 1 shot or single targeted, but I'm not sure about dopp chat.
Why Exterminator only? Scientist may side with the town, especially if they can obtain enough protection to finish their job. Exterminators can't bargan with anyone.