In reply to supersteve:
Unfortunately your best option is changing the bars. Unless you are very lucky and the manufacturer of your bike / handlebar have made oval clamps which specifically match your handlebars.
Don't risk a bodge here, if it fails, you will lose control of the bike and there is very little between your face and the floor.
Profile designs make some decent value bars that have an extended centre section where you can safely clamp aero extensions, but still a nice comfy oval sections where you rest your hands. I had to do a similar swap on my wife's bike recently and this was the best I found at the low budget end.