If I'm reading your sugestion right...
The idea is to use a short FL projection lens, but using lenses to manipulate the image to 'appear' smaller to the projection lens.
Close, but no cigar. You simply can't manipulate the image that way. What you'll end up with is a completely unfocused blur of light.
You can't change the shape of light with a lens. The best that it can ever be is a focused enlargement (or shrunk) version of what you start with.
So in your diagram there, light leaves the lamp, goes through one fresnel lens, the LCD, and the other fresnel lens, then through another lens and on to the projection lens, is that right? It looks goon on that diagram, but consider instead this:
This is more or less your diagram, but with a representation of a black LCD with 3 small coloured points on it.
Click to view attachmentBecasue you won't actually have an IMAGE at the focus of the lens, but rather just a collection of light, what you'll get at the other end is... A blurred collection of light. You might be able to make out some of the basic shapes in the image, but that's about it, really. (Note that this is actually an optomistic representation, (In that it actually DOES focus SOMEWHERE) but you get the idea.
This is how it would turn out in the end.