Currently I'm anything but consistent, but looking back over the years of trial and error my best advice is to not be hesitant to ball up and move inward rather than ball down too many times and trying to stay in the same area of lane too long.
Once the starting area gets "torched" virtually any (resin) ball is going to surprise you at how much it moves. I see bowlers trying to throw it faster than they really can with any consistency because they're afraid they'll miss the head pin altogether and be embarrassed.
If your typical house shot becomes over/under then just tell yourself to make the "big" move inward with the stronger ball that handles oil better and blends the pattern out more (front to back AND side to side). As you move inward mentally draw a straight line to your breakpoint down lane and hit that spot instead of looking at a target at the arrows and creating too steep of a launch angle and possibly losing a few to the gutter.
With a little practice your confidence will grow, and you'll become that versatile guy you have always envied. Your drive home will also be more peaceful because you won't have to think of all the reasons your scores went from Heaven to comparative Hell. I bowl a second shift league on Tuesdays and after all these years I have come to learn this principle more times than I will admit to. Hope this helps someone to improve their scores, too.