Any reason not to run my Macbook Pro upside-down in clamshell mode? My MacBook Pro gets stupidly hot when I'm working on it normally (not clamshell). I am worried that the heat could damage the screen if I use it in clamshell mode. 

I thought that I could place it upside down (in the sense that the Apple logo and LCD panel lie flat on the table) on a non-slip surface so that the heat would vent right out of the (now) top and away. Could I knacker the fans by running them upside down?

The laptop is a 15" MacBook Pro with retina display.
You can place the Mac in whatever orientation you like during clamshell mode as long as it's supported and protected from falls.

I really like the Book Arc stand so that the trackpad area is by the table and all the warmer section near the hinge is up and exposed on all sides to airflow. If you really need maximum cooling, try the SVALT D cooling stand.

Your proposed mechanism should be measurably cooler when you have the CPU generating maximum heat and for some reason the airflow / ambient temperature wasn't cooling things as much as you had hoped. The air trapped in the LCD panel can have a fairly good insulation value and if the surface is soft, airflow under the feet is diminished.

The Apple fans are high quality and likely magnetically suspended or have so little play it's not a concern unless you have shocks or other accelerations.