BTW, just popping the housing off of my unit fixed it, and it stayed fixed (at least for the moment) when I replaced the housing (karma?). My motor has been making noises for a while, but suspect that it was one of the two microswitches failing rather than the motor itself.
I have the plastic-housing version of this unit. I removed the (four) rubber feet, but underneath there was nothing but blank plastic, even though the structure looked exactly like there should be screws there.
The solution: the plastic housing is held in place by four latches around the base, each visible in a slot between the housing and the base. Pry them apart, and you can then pop the plastic housing off. (You may have to work your way around several times before the first latch doesn’t re-latch while you’re working on the other ones.)
Which of those two lensed units does the distance sensing, and which does the video? Would you open them up? (Or are you trying to preserve your gaming abilities?)
If you will be reusing the glass, with new adhesive, then you will want to remove the old adhesive. This is a bit of a pain, as alcohol doesn't work, and you need to be careful to avoid damaging the black screen border, which is black paint on the back (adhesive) side of the glass.
To remove the adhesive, note that it is actually a thin film with rubber cement on both sides. First, use a razor to carefully pull up one corner of the film and gently peel it off of the glass. If you are gentle and slow, the underlying adhesive may also come off; if not, then rubbing with your finger or a hard rubber eraser will do the trick.
I just removed, cleaned, and replaced the display glass on my MBP without removing the display, and it turned out to be much easier, including removing the bottom edge of the glass. Perhaps this was because the original glass adhesive was failing, with most of the top edge adhesive no longer doing its job, and in most cases removing the display will make the task easier. However, I'd suggest doing the glass only first; if you find you can't remove the bottom edge of the glass then you can remove the display and finish the job.