After reading your post, I ordered the Meike grip and it arrived very promptly. The price including shipping was only $49 Canadian! I have put it on my D7000 and enjoyed using it. You have described it perfectly including the flashing green SD light when the grip is "rocked" slightly so I will try your paper "shim" out to see if it eliminates the slight rocking.
As other people noted, the little battery tray locking tabs seem very fragile and have to be handled with care. They could get broken off easily. Meike should put metal tabs on instead. For the money, this is a great deal!
I decided to configure the camera to use the battery in the Meike grip first before using the battery in the camera. This way, I only have to remove the grip's tray to charge the battery in the grip instead of removing the entire grip to get at the battery in the camera. Configuring which battery to use first is done in the d Shooting/Display d14 Battery Order "Use MB-D11 batteries first" menu item.