Sandwich the plexiglas between the emblem and the belt buckle backing. No need to bend it...just shave it to match the arc of the backing. Only the exposed edges need to be clean cuts...the faces against the emblem and backing can be rough surfaced.
It will probably help smooth out bright spots if you put something reflective against either face of the plexiglas piece, except in the spots with the LEDs are. Might even want to try using small surface mount LEDs and carve small, fitted recesses into the plexiglas for them.
I would also cut the edges of the plexiglas at a slight taper, so that the base is slightly wider than the face. That way, even though it's behind the emblem, you'll still see some of it around the edges (inner and outer) of the actual emblem even from a straight-on viewpoint.
Another option is to replace the emblem itself completely. Bright enough light will come through reflective paint if the paint is applied thinly. You could mold some clear resin to match the emblem, then paint it silver. During the day, you have a chrome emblem. At night, with the headlights turned on, you have a lighted emblem. LED hotspotting will definitely be a tough issue with this method, though.
This guy made his own "stealth" silver signal lamps for his 3 series:
http://home.comcast.net/~matth...x.htm
You could use that technique to achieve the illuminated painted emblem.