I need to make a plane shine light only in one direction (or a very narrow angle range) like a spotlamp, or a projector but I don't want to use a spotlamp - I need a wide beam of light, that doesn't spread out in all directions. Spotlamp would produce a tiny cone of light, not a wide beam.
As you asked for a wide area :
Use an area lamp framed by an open cube (or another shape).
The lamp material is constrained by a constant falloff so that you have sharp borders on the light projection.
The open cube, is hidden on the rendering and diffuses nothing, due to this setting in its object properties :