Any chance you can drill from the bottom? I doubt it, but thought I would ask.
I just did something like this last night, but my solution won't work as well for you. There is a 'punch tool' that is made to cut through material like carpet when using a hammer. I used that to create the holes, then I could put a drill bit through them to drill into the metal.
You might be able to do something similar with an awl. Try to open the holes up in the carpet as wide as you can with an awl, then you can have space for the drill bit? You could do this by lifting the carpet and pushing into the tunnel opening maybe...
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