As per Sheldon's recommendation, I bought
a poppy seed grinder:

http://www.cooking.com/products/shprodde.asp?SKU=158486

Maybe I bought the only one! They're out of stock now.

I asked for something like a meat grinder, but more fine grain.
That's sort of like the effect this machine achieves, but the
mechanism isn't quite like a meat grinder. It's more like
a minature grain grinder, surrounded by a collar so all the
ground stuff goes in one direction. The material is forced
by a screw feed between conical grinding burrs.

Running dried apricots through it, it produces a nice
paste, less grainy than my meat grinder. Closer to
being mashed. Running almonds through it produces
a powder. It seems that this machine was designed
to avoid expressing oil from any seeds it ingests.

It's easy to clean. My main complaint is that it is
contaminating the food with some gray stuff,
probably iron from the exposed iron surfaces.
I've run most of a pound of dried apricots through
it, and the contamination is still present though
it is much reduced. I'm hoping it'll go away
completely with enough use.

The texture it produces is unique. Even if I don't
use it much, it will be valuable to have this capability
available to supplement the range covered by the
meat grinder.

I'll have to try running some poppy seeds through it.
Here's some interesting recipes:

http://www.erowid.org/experiences/exp.php?ID=4613
http://www.erowid.org/experiences/exp.php?ID=24436

They would seem more appetizing if not for the throwing up part.