I took a different approach:
- Mask off the holes to protect the carpet.
- Use a nail and vacuum to clear out a 1/4" to 3/8" inch area under the floor through the hole
- Fill that area with glass strand and polyester resin.
- Coat the screws with a thin coating of a release agent (WD-40, melted wax or ?)
- Insert the screws half way into the holes.
- Remove the screws after the resin has set.
You now have a threaded plug under the floor that is very strong.