Oil overfill and system too lean bank 1 related?

What is your question?

I am not mechanically inclined at all but ill do my best to describe my situation. About a month ago I had my oil topped off at a family members dealership. A coulpe days later my jeep started to run pretty rough. I dont know why its taken me this long to see the timing and wonder if its related. I checked my oil yesterday and it is way beyond the safe line. I pulled the code and got P0171 which is system too lean bank 1. I understand what that means and the number of isssues it coukd be. The dealerships mechanic suggested I lower the oil level and then drive it to see if it burns off any oil that may have soaked any sensor before paying to have it repaired. Obviously it makes sense to lower the oil level before driving it again but does what hes saying make sense? That best case scenerio this could fix itself? Right now im getting about 4 mpg, struggles to accelerate from a stop and idles rough. Im also overwhelmed by the smell of exhaust and there is a grey/blueish smoke. I understand those symptoms match P0171 anyway and dont necessarily narrow it down to what specifically. Id love to be able to pinpoint this and keep my repair bill as low as possible.