I have created a part that - at least with Cura - seems to be unprintable without adding builtin support

The attached STL would need support "Everywhere" in Cura, but since I need to insert two M5 hex nuts at Z=24mm, I can't use that type of support because it would fill the hole for the hex nuts. Is there a trick to get around this without buying Simplify3D...?

Best regards,
Reiner