Drat... I see what you mean about the edge pieces overlapping. They sure don't make it easy for you, do they??
The only other thing I can think of is using a linear actuator made for opening / closing mini-van rear hatches, like the one pictured below...
(from the e-bay auction at
SKF Linear Actuator - eBay (item 200519614306 end time Sep-21-10 08:30:37 PDT))
Unfortunately, these are typically $50+ (though this one seems to be reasonably priced in comparison)