Slic3r settings for flat slopes on top
This seems to be a recurring problem with Slic3r.

Slic3r appears to have problems with perimeters that are not attached to infill.  I suspect that it is getting confused on what is the inside and what is the outside.  I know that seems a bit silly; but as you slice an object with indentations (like the bunny's face) then the perimeter can cease to be a simple closed shape and it gets confused.  If you use a viewer to step through the gcode layers around the place it starts having problems you may be able to see what is going wrong.

Here are a couple of examples of why I say this is a recurring problem with slic3r.  I also recall seeing a video that showed the problem but I can't remember where.  That was one of the reasons I don't use slic3r.


Reported on Sic3r Git in 2012 - Can't tell for sure if this was ever fixed
Infill Perimeter issue in 2015


Here are three options that may work


Use a different slicer for this specific condition.  Every product is going to have vulnerabilities - this may be one of slic3r's.
Increase the perimeter and top and bottom layer thicknesses.  Making them thick enough it will bridge the problem areas.  Use a gcode viewer to inspect that area to see if it fixed the problem.  That way you don't waste material on another fail. It sounds like you may have already tried this but you didn't like that it made the model stiffer.
Repair the STL file using an application like Meshmixer.  Maybe you will have to get the file close then tweak it where it doesn't.  Here is good article from PinShape repairing and STL file.


Good luck, hope this helps.