I see digital noise with the EX3 even with no picture profile and gain set to 0db.

For example:

http://www.b-scenefilms.com/ex3noise.png
(admittedly, this is a 200% magnification of a 1080p frame...)

Is there any setting that I am not aware of that will reduce this?

Try to set the gain to -3dB... (and enhance the light)...

OK I will give that a shot. That example actually had plenty of light - was with ND2 up.

OK this is with -3db gain. no PP, f13, ND1 (iris adjusted just to the point of no-zebra):

http://www.b-scenefilms.com/ex3noise2.png

Still LOTS of noise...

Also try the same setup with ND2 or less light.

Stopping down below f5.6 will soften the image. The noise may not go down, but the picture will look crisper with the same detail settings.

Then drop the detail to -10/-30 range and shoot again.

OK this is with -3db gain. no PP, f13, ND1 (iris adjusted just to the point of no-zebra):

http://www.b-scenefilms.com/ex3noise2.png

Still LOTS of noise...

You are underexposing try opening up the iris by one stop or more.

You do not mention what your zebra values are. Try 85 or 90