Try using another image as a reflection-image layer.
1) Open the image as a new layer.
2) Select you mirrored pieces layer - Alpha to select all your mirror pieces.
3) Select>Invert.
4) Select the reflection-image layer
5) Delete
Now lower the opacity of the reflection-image layer real low so you can barely see it.It makes a reflective glare like you would see in a framed photo on the wall.You may want to try making a triangular corner selection on any of your mirrored pieces and coloring it white and setting the opacity to that real low also.Makes a light reflection. I also created a PATH fromthe selected mirror pieces so you can use the selection at any time without reselecting the pieces. You can do this with channels also if you prefer.
I added an image example for you to compare. The lillies image i used for reflective-image layer is not really a good image for this. Something with more light would be ideal. Like a room full of windows.

XCF workspace file is attached also.