I've just spent that past couple hours with Jamie LeJune, a master colorist who has figured out the problem.
Even thought my source ProRes file was exported rec.709 it's actually graded in a BT.1886 color signal path. When we switched the DoM color setting to Rec.1886, the test DCP looked correct:
Top left - ProRes source
Top Right - DoM Rec.1886
Bottom left - DoM Rec.709
Jamie said it's really great you have user options to select the output colorspace. This is impossible to do in Premiere Pro or FCP, though it is possible in Resolve.
I've been working in Premiere Pro and even though I've exported in Rec. 709, Premiere is internally maintaining the BT 1886 colorspace. It just doesn't give any user feedback or control during export.
I've learned more about color management this afternoon than I've known in decades
I've confirmed that the Rec.1886 setting (maybe you should rename it BT.1886 to be exact?) looks correct in the monitor. We'll confirm our next DCP in a cinema to be sure we're definitely solved the problem.
I should note that I'm did this test with the current release version of DoM. I just downloaded the OpenGL fixed version of DoM Player and it's now displaying gamma properly with OpenGL:
Hopefully we've solved both problems! I'll let you know how our cinema test goes. Many thanks to both of you for your help!