Do you back into your garage, or drive in going forward? I just checked in my own garage, and one thing I noticed is this. I usually back into my garage. When I do that, and the garage door is raised, the door only goes over the front half of the car. So if the car is already backed up into the garage, raising the hatch just needs to clear the ceiling of the garage, and not the door itself. If you back your MDX into your garage, clearance might not be that much of an issue.
Also, while my measurements may not be useful to you - because each garage may be different, and my MDX is a 2004 so it's not exactly the same dimensions as yours - I measured, and here's what I found. My garage door is 7' high (84"). When it's raised, the vertical clearance underneath it is 86" (IOW 2" more clearance than the height of the door itself). (The arm that raises the door requires an additional 3-4" of clearance so it might be as low as 82".) When the hatch door on my 2004 MDX is raised, it's 78" off the ground. So if I wanted to, I could open my garage door and open my MDX hatch, and it won't hit anything if I backed into the garage with the open hatch underneath the garage door. Like I say, these measurements aren't exactly the same as yours would be, but it shows you how to do the calculation to make sure it clears.
HTH