"can I make the GRUB that came with the Ubuntu Desktop to control the boot
sequence?"

I'm certain you can. But it may require some magic to get this on the MBR. The
MBR needs to know the location of the GRUB file you wish to be the controller
(for lack of a better word). If there's a way to force a write to the MBR that
isn't destructive, then this sounds like the way to go.

Once the MBR accepts that your Ubu Desktop GRUB file is the one to look at, it
should be smooth sailing from there.
Again, I only have the theory in my head, and not the actual steps to do this.
Google is your friend.