I fought this condition recently in the Greater Louisville Bowling Association Masters tournament. Inside of 10 was on fire on most (not all) pairs, even on the fresh, and outside of 10 was flooded. Very flat pattern as well in those respective zones. Depending on the pair, I fought it different ways. I had a couple pairs that let me move right and roll it up the boards in the heavy oil, using the Norm Duke type of approach of just floating the ball and letting the ball roll hard and do all the work. On most pairs, however, I moved inside and played them tight with some speed. This gave me more miss room since the majority of people were playing the track area, which meant they broke down more predictably inside than out where very few people were playing. On pairs that weren't quite as burnt, I used a Second Dimension with just a light coat of polish, and kept my hand behind it to keep it from jumping too hard downlane, just keeping it around the pocket. On other pairs that hooked more and earlier, I used a strongly drilled Mars to get length, but have the ball still roll off the spot. For what it's worth, this approach got me a 3rd place finish in the tournament since it kept me out of trouble better than everyone else. I only shot around 175-210 every game, but that's all it took to win since I wasn't leaving as many splits and washouts as the guys trying to get too fancy or creative.
