Here's an idea that should work, though I don't know anyone that's tried it.
Cut the tops off the supplied screws, or some screws of your choice and glue them at the E&G's in the holes.
Mount the E&G flares following the instructions. They use the same holes underneath as the factory flares and are very solid with only those screws. You can also add some stainless screws and/or double sided tape underneath for added stability.
Here's a link to my install write-up:
E&G Flare install