I have been waiting years for this question. Go to the video store and rent one of those black and white gangster movies. Watch until you get to the nightclub scene with the cigarette girl and there it is. That cigarette tray is the perfect solution to your problem. You may not even need the velcro.
Use a serving tray, the same kind you would use for breakfast in bed. This tray would have legs, thus self-supportive but not raise your console to an uncomfortable level.
Trabasack Connect range, are lap trays with a surface you can velcro things to, perfect for games controllers to keep them steady. Trabasack is a bag too so great for gamers on the move