I tried a page fresnel lens.  

One layer had a focal length of ~35cm.  Image quality was ok, but the resulting image was tiny unless projected over a very long distance.

I added another layer in the four possible configurations.  Two looked ok.  Quality was not terrible, but was degraded from a single layer.  Focal length was about half of what it was at about 17cm which makes sense, and the image was roughly twice the size for the same projection distance.

That's still pretty far off from the less than 40mm focal length that I need here.  Unless I get a much stronger fresnel lens, I think they are not going to work here.

So... I tried the flashlight lens.

It produced an image 1 meter across at a distance of 1.5 meters with the subject about 17mm from the lens.  That is a little more than I need actually.  I was shooting for a 1 meter image at 2 meters.

My highly technical test rig.  I picked the first sem-transparent thing I found with something around the right size.

It is roughly the right shape though for this application.  From my research the projection lens should be plano-convex, aka, flat on one side... with the flat side towards the projected image.  Incidentally, that's the way it looked the best too.

Problem is it's a garbage lens and you can't focus the center and edges at the same time... ever.  I think if the projected image source was smaller, it might still work.  I would probably have to generate real slides then as an inkjet would cease to have sufficient resolution.

Extrapolating from this experiment to fit the form factor I've generated thus far, I would need a plano-convex lens with a focal length somewhere between 20-30mm.  This just about matches the math I found on the subject too.  I'll look around.

EDIT:  I tried adding the fresnel lens for collimation between the light source and the image source, and it looked terrible.  The lines from the lens were very visible in the projected image and brightness was barely affected.  I think just a diffuser will be going in its place.