Use servos and do a search on 555 servo controllers - you can use a couple of these to ahve predefined up and down positions for the servos and the circuits cost pennies to make. Servos are self correcting so will keep the screen in place but i would use some rubber bump stops behind it for extra protection.
To solve the reach problem there are several ways:
1. have the screen face up when closed (not idead for dust etc) but to solve this make a cover that is hinged at the rear and gets pushed up by the screen opening and also provides a sun shade.
2. have the screen on a slide or rack system so as it rotates it slides forward (can link these two motions if you are crafty.
I am using this type of control system for my, dare i say it, motorized screen (which hopefully isn't gonna end up as vapourware)