I worked some more on the combat challenges. Progress was still slow; I just couldn't seem to get the points required. I turned to google in my hour of need and saw the most interesting video on youtube. They got the points, more than enough, just by keeping the combo going. They weren't doing any takedowns, no gadget quickfires, nothing. Just an incredibly long combo of standard attacks with a beatdown at the end. I knew that breaking a combo is damning, but I thought to get the big points you had to go for the variation bonuses as well.
It was a revelation.
I tested this method with all three characters and it worked like a charm. Those thugs won't know what hit them tomorrow.