Not sure I understand the exact question/problem.
If the laptop is in an incovenient location, why? Do you put it there
after the shutdown? Do you normall use it in that same location?
I'm not familiar with the control-eject method of shutdown, but since that
does the job, I don't understand why you seem surprised that the screen would be dark or that the machine is actually "Shutdown." And I am also unaware of any way to start up a Shutdown machine without using the power button.
But perhaps you simply want to put the machine into a sleep mode that will allow you to start working again with the opening of the lid. There should be some help from MBP users about the various sleep states that it is capable of, one of which should solve the problem.
While I can see a problem with carrying a laptop inside a pouch/case while still on for too long a time could cause heat problems, I don't understand how leaving one in any sleep state would be cause for concern when it is sitting in the open on a cart/desk. I stand (sit?) ready for correction on that front, however. My only real experience has been with an older iBook which is hardly ever Shutdown while on my wife's desk. And that may be much different for a MBP model.