This campaign "reach" number is mostly a vanity metric, but could be useful for justifying costs to brands.
So just consume the filter streaming api with your chosen hashtag. You will get all the tweets, or at least some and a measure of how many you missed (limit notices).
For every new user in said stream, add the number of her followers.
It's so easy you could write the code in the length of this comment. Of course, if you want to avoid counting duplicate followers, you'd have to do an average of 1-2 additional calls per user.
To justify cost to brands it might be easier/more 'sellable' to insist on actual, measurable engagement (links clicked, tweets retweeted, tweets favorited etc.) around their own tweets. I'd worry about unrelated tweets (i.e. sharing the same keyword but about something else altogether), or either bad publicity being accounted for.