Is there a technique to capture conventionally-printed pictures (i.e. screened
images printed on an offset press) without getting the moire effect from the
dots?
Sure, there are descreen procedures for the moire, see
http://www.scantips.com/basics06.html
The simplest trick is to use scanning resolution as high as you can bear, at
least 300 dpi, and 600 dpi is better if you can stand it. A full size color
page at 600 dpi is 100 MB, but this may be feasible for a 3x4 inch photo area.
But 300 dpi will help a lot (whereas 75 or 100 dpi is the absolute pits).
Then resample the image to the smaller desired size.
High resolution and resampling smaller is a major part of the descreen
procedure anyway, and it may be enough by itself in many cases.