I fought the same kind of thing all season in my two leagues at one house that puts down one of the easiest oil patterns in the state. For the first 1.5 games, you have to go out of your way to miss the pocket (and I actually usually play the lanes pretty similar to how you described! Just move everything about two boards right). However, since so many people play the same part of the lane and burn up all the oil there, the shot suddenly gets very wet/dry and the outside part of the lane is just on fire. I have had to attack it a few different ways.
If the outside part of the lane had dried up so badly that it felt unplayable over/under, I would move left with my feet and breakpoint and play in the heavier oil in the middle. If few people were playing there, I'd use my Cell (5.5" pin to PAP, pin under middle finger, MB in a fairly strong position) with a
very light coat of polish, and focus on rolling it slower and making sure I didn't use too much axis tilt. If there was more traffic in the middle of the lane to help break it down, I'd use a Gravity Shift with a very light shine, or a more highly polished Second Dimension (both 5x5 pin up, slightly smaller pin buffer on the 2D and it also has a P3 location x-hole), or if they were hooking a lot inside, I'd throw my Reign and avoid the dry outside. The drier they get inside, the more I needed to pay attention to my hand position to make sure I got a little extra pop on the backend.
If the outside part of the lane was getting a little less traffic or the transition from oil to dry was more manageable, I'd keep my breakpoint outside, but switch to my Reign and increase my speed and to a smaller degree my axis tilt. Sometimes this would give me a hook/set kind of reaction if they were particularly dry, but this works pretty well sometimes (especially since it means misses to the right and into the friction will not hook through the face since they burn up earlier!). And of course, if they just got too dry, I'd throw plastic right up the boards, and even though I've got very little hand, it still works if there's enough friction. The last week of my Tuesday league, they got so dry I threw plastic and covered more boards with it than I did with my reactive stuff on fresh oil earlier that week.
