I haven’t tackled the middle Z yet, but I have experience similar issues in the past. I suggest trying a different slicer. I have recently seen a few reviews and Slic3r seems to always be rated low. I have used only Slic3r up until about a week ago, so I decided to try another slicer. I just started using Matter Control and I’m quite impressed with it. I’m using it to print my MPCnC parts right now.
You could try adding some Z lift. You find this in the Printer Settings under Extruder. I used to use 0.5 mm with Slic3r. This lifts the Z axis when the head travels.
Hope this helps, good luck!