I also said that " I know that the second Write() call which outputs to STDERR does output a valid pdf file.". I didn't think anybody would find it useful for me to post the contents of the entire pdf file. Here's the first few lines of output produced from the second Write():
%%CreationDate: (Wed Jan 29 18:07:37 2003)
And here are the last few lines:
%%BoundingBox: 0 0 611 791
UPDATE: I now realize this isn't what a pdf file looks like. This is what a postscript file looks like. Either I have totally missed the boat on how to use Image::Magick, or it doesn't quite work right for all combinations of conversions yet. In any event, thanks to everybody for their help, I've found a better solution to my problem.