Out of curiousity, is it over the duct run? That would also make it inaccessible from underneath? I assume the duct is solid, not 3 sides attached up to the floor to complete the duct. I haven't stuck my hand down there.
What I thought I would end up doing is pulling the carpet. Routering or morticing out a strip to attach a strip of metal with small screws on either side. If the seam is on the duct you could also try to get some adhesive between the panels.
For us the main floor does not have any creeks yet, just the stairs.
