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Fun, but:
I'm afraid there's a missing piece of optics in the proposal. If you went out with binoculars to look towards the tower, all you would get is a view of the projector lens, the same as sitting in a movie theater and looking back at the projector. A system like this needs a condenser or relay lens, or a diffusing screen, at the point where the "virtual screen" would be. The concept might be rescued if the image was actually projected on a screen close to the tower, and then the viewer was provided with a zoom-lens light-amplifying telescope to view the projected image.
This does not mention the problem of the high level of bias light due to daylight washing out the image (even if infrared). Perhaps it would only be used after sunset?
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