After an afternoon exploring every possibility that came to mind I hit on the idea of buying a plate stand for the iPad. I'm using it now. It lifts the device about four centimeters above the table, will not topple backwards or in any other direction, looks pretty cool and cost exactly 1 euro. I bought a medium sized one, plastic, in black. Here's an image of the sort of thing it is:
http://cliffordsweb.com/web2/carlton/images/hearthside/IMG_4602.jpg
Styles no doubt vary.
http://cliffordsweb.com/web2/carlton/images/hearthside/IMG_4602.jpg
Styles no doubt vary.