Support for 1/16" offset

I’m printing a lid for a project box and I’m printing it upside down so that the lid top gets a nice flat surface to print upon. This lid has a square cut out window in the center with about a 2" border inside of it that is offset 1/16" off the print surface. I used auto support on Slic3r and it doesn’t seem to want to put support under this offset area. I changed the setting to support the first 50 layers or so which is far more than needed and it only added support at the very rim of this offset. During printing, it basically bridged the distance between this rim support and the outer lid area, leaving stringy filament pieces laying across that aren’t as tight as the rest of the box. Is there a problem with wanting to add support for such a small dimension (1/16") ? Is there anything else I can do to customize the support?

Did you uncheck the box labeled “Don’t Support Bridges”? If this is checked, it will not print support under what Slic3r considers a “bridge” which is what I believe you are describing.