Since the "overflow: hidden;" property does not properly work on the iFrame itself, but seems to give results when applied to the body of the page inside the iFrame, I tried this :
iframe body { overflow:hidden; }
Which surprisingly did work with Firefox, removing those annoying scrollbars.
In Safari though, a weird 2-pixels-wide transparent line has appeared on the right side of the iframe, between its contents and its border. Strange.