hmmmm... there are oversized clamps and bars with non-round tops, but I'm not sure if there's oversized tubing in the "business end" of the bars?

There used to be that really thick foam stuff you could put on your bars. I don't even remember what it was called or whether it might still be available. I have used two layers of cork in the past. What type of tape are you using now?

Are you sure it's the diameter of his bars that you like, or could it be the shape (bend, width, reach, drop)? You could find out if his handlebars are made in a size to fit you.