For now, if I were a member of Congress I'd zero out the IRS's travel and conference budget -- the service spent tens of millions of dollars on videos spoofing Star Trek, Gilligan's Island, etc. in past years, for conferences held in cushy locations like Anaheim -- and look at other ways to make the agency pay.
Targeting Americans is unforgivable; covering it up is worse, and if the IRS has made it impossible to target the individuals responsible, then the IRS as a whole should pay the price. That's not an ideal solution, but such misbehavior should not go unpunished.
My view is different. I don't think the IRS or its employees need to be punished... bureaucracies are best understood as psychopaths whose fixations and behavior are inwardly focused and governed by their internal rules and culture. Like psychopaths, you can't really "reform" them. Fortunately, unlike human psychopaths, you can disband a harmful bureaucracy and start over. I've called this institutional capital punishment, and I think it's the only way to properly resolve the IRS debacle.
Obviously America needs an agency to collect tax revenue, but the IRS -- its rules, its internal culture -- are so broken that it can't be trusted to do the job any more. This doesn't mean that the employees are bad people, but they're working in a bad, broken system. Rather than trying to fix the psychopathic system, just "execute" it and start over from scratch with a new tax collection agency.