Hi Pete , that's exactly what I tried to do. Unfortunately it did not work.
However, after reading this post: viewtopic.php?p=310994#p310994
where Eliasthecollector93 mentioned a helicopter cube, I think I figured out how to solve the situation:
The 2nd image above, where the corners are in the correct positions is equivalent to:
heli.jpg [ 55.39 KiB | Viewed 383 times ]
and anyone familiar with a helicopter cube ought to be able to solve that state. The square corners and unattached triangles luckily solve themselves and don't require any other work.
So there is a way to get out of the state shown in that first picture without jumbling.
I think the Dayan Gem VII is like a supercube of the helicopter cube, in the sense that the triangular "center" pieces of the helicopter cube now have a second color on them making them uninterchangable.