1969 Cuda Grill Resto...any tips/tricks??

Reviving an old thread here, I think Im finally "ready" to make these grills a winter project.
One thing Ive noticed is that there are rivets that hold the plastic oval to the outer most chrome piece. I have spoke to another member and he mentioned that I could just drill them out but there is no chance of "re-riveting" it back on.

What has anyone else done for this part of the repair?
Im assuming in order to do a proper fix the plastic oval that the chrome has to come off.

Ideas??
Sorry for the lousy pics, but hopefully you can see the rivets in the pics