Yep, strategic use of increased reps would work. Look into Alwyn Cosgrove's Afterburn program or Craig Ballantyne's Turbulence Training. Also look into using "finishers" at the end of your workouts. Dan John has had some awesome articles on here about them.
Nutrition-wise, gradually cutting back on carbs will have a relatively faster effect on dropping weight (not necessarily fat, initially.)
In general, as has been said, move a little more, eat a little less, and do neither to an extreme.