Ugg.. so I created a hit using mturk's own designer interface with the following HTML:
<h1>Please make this sketch look good.</h1>
<p><img src="http://example.com/my_sketch.png" alt="" /></p>
<p>Upload your version when you're done. Thanks!</p>
<p><input type="file" name="drawing" value="" /></p>
This does not work. Apparently.
The results have a "drawing" field, but it just shows the filename of the file that was uploaded. The actual file is irretrievable.
My mistake is a repeat of a mistake made by someone on this stack overflow question.
UPDATE: so, I was able to get a couple of these images using the NotifyWorkers API call, telling my workers that the drawing was lost, and asking them to e-mail it to me.