My ideal plan would be to revamp the Circle system from top to bottom.
Instead of using it as a permanent residence for mages, it would be a training center. A mandatory training center, but a temporary one. I'm in favor of requiring all known mages to train and eventually undergo testing at the Circle... I think the Harrowing is fine in spite of being dangerous, but at the very least the mage should be told in advance what they'll be facing. It would be voluntary, but they can't leave the Circle until they pass it. The training that I mentioned would include more than lessons in spellcasting. The primary focus would be learning to recognize demons in the Fade and how to resist their influence. After all, the biggest problem with mages is the potential to become abominations, not the possibility that they may choose to abuse their power... anyone with weapons can threaten the peace, but if a mage becomes possessed, their will is overwritten by that of a hostile demonic force.
So... what happens once all of this is done? Well, whenever the mage proves that they are ready, they are free to integrate back into society. The conditions are that the Circle keeps a phylactery to track them down if they need to, and the mage must agree to monthly (maybe every other month) visits by local authorities to make sure they still live in the area. They aren't allowed to move to a new city without first informing the Circle, but they are not in any way restricted from moving. This is merely a way for the authorities to know the general location of every mage and the concentration of mages in each city, so that law enforcement can be ready to deal with any issues that may arise.
Wait, law enforcement? Who's in charge of all this??? IMO, the Templar skills are too valuable to be lost to the world, regardless of their Order's reputation. Assuming that such a system is agreed upon, I'd have these skills passed on to special agents within the city guard. This group would be mainly responsible for dealing with whatever threats mages pose, conducting monthly inspections to make sure that a mage hasn't moved without notifying the Circle, and hunting down rogue mages using phylacteries. They would be very similar to the Templars, but they would be strictly reactionary and would have no intrinsic authority over mages. Furthermore, I think that mages should be allowed to join this order, as well as the city guard, if this were to have any hope of success. Not only are mages capable of learning many spells that can nullify or counter magic, having mages within the city guard would do a lot to repair the misconception that they are untrustworthy as a rule.
Now, I realize that I'm only describing this because the mistrustful nature of Thedas's inhabitants has been mentioned, so how do the mages cope with that? This one sounds a little tricky, because there are a lot of variables to account for. The most I can say is that if mages slowly become more visible among the population (guardsmen), while simultaneously living in peace without their abilities being made public (normal citizens), normal folks should eventually get used to them. Crime is a fact of life, so this doesn't guarantee that normal people will leave known mages alone... at that point it's probably up to the mage to use some of that power in self defense. So long as mages are not punished for using magic to defend themselves, it should be treated like any other violent incident. Acceptance of mages wouldn't happen overnight, but within a few generations I can see it becoming reality, especially if the Chantry isn't constantly in the background reinforcing the negative image that they've been using for centuries. Since mages are currently under lock and key, all the common man has to go on are fuzzy memories of a local child accidentally starting a fire when their power first manifests and the Chantry's propagnda. Once they have concrete examples of mages who have no wish to become tyrants, their prejudices should fade away.
I may have left out a step or two, but this post is pretty long so I'll leave it at that...