Support problems on small object

[3D-Ken 0]

The attached .STL is just a test piece that is part of a much bigger print.  The protrusion is very small.  The whole piece is only 6 mm tall, with an arc radius of 1.5 mm.

 

I can print the test piece vertically and it comes out perfect. However, it needs to print horizontally as part of the bigger object.

 

I determined that it needs to print with the smallest layer height possible with supports, but no matter what I do with the supports, it never comes out with a useful print.

 

Are there things I can do with supports to make this work, or am I just asking the impossible?

Using a Prusa i3-MK3.

 

P4.stl