Hi Jamie,
first, welcome to this forum!
As far as I am convinced, there is no such thing as a single case for your Qu24 mixer and 19″ racks for all your other gear. If you were talking about a QU16 which is a rack mountable mixer then that is possible, and heck anything is possible, but personally I would never want a single case to house all that stuff.
Your Qu should be in a separate case. I understand you want to take off one lid and have virtually everything already connected.
A Q-Pac or Mackie DL32R would be far more practical to me.
.02