It sounds like you're on the right track. If you can get the weight of the cable off of the connector somehow (either by shifting it to a support or by shifting it to another cable), the plug should be able to support its own weight and stay in place.

This is a problem can is only going to happen more and more as LCD and plasma displays spread and HDMI sources join them. Manufacturers understandably don't want to use the same horizontal orientation found on the back of source components for these flat panel displays, but I think a display manufacturer could make a lot of consumers very happy if they took that vertical orientation, rotated it 90 degrees, and provided a built-in velcro strap or even just a simple support peg a few inches away to take the weight of the cable off of the connection. The combination would make it much easier to keep HDMI cables connected, and the cost would be very small. Heck, the support peg would potentially be free - it could double as a sprue point for the plastic mold if they worked it right.