Having spent some time in government and on the expenditure review committee, I don't remember this species of person called a neutral program evaluator. I'm not saying you're wrong, but I would have thought that even if you have that person, the committee will get what the government wants it to get.
Why not use the Parliamentary Budget Officer or some other independent body that works for the committee—not for the government—to spearhead this thing, possibly in conjunction with these people you've described? I don't think you want all the determination of the reports to be put into the hands of the people running the program or even of the government.