In the diff, you'll see three small bevel gears and a little “Y”. Instead of mounting all three of them on the little Y, mount only two. Then take the third and wedge it between them, making sure they sit flush (they sit perfectly flush when properly positioned). This will make it impossible for the large bevel gears to rotate at different speeds, locking the diff up tight.

Look carefully at the picture.
It's totally reversible, with no messy glue or gunk to mess with.
When you want to unlock the diff, simply put the bevel gear back on the Y