Fix: You could do all of the following, or - as syphilis points out below - run the ppm utility which is available with Strawberry Perl. ppm install ImageMagick.ppd works a treat. Thank you, syphilis! Lengthy, unnecessary, somewhat inaccurate suggestions continue below.

A "quick-fix" which worked for me is to install PerlMagick using the ImageMagick installer (which fails, since Strawberry Perl doesn't have a ppm utility). But the PerlMagick files are stored in ImageMagick's folder, and you can copy them from ${ImageMagick's folder}/PerlMagick/blib directly into C:/Strawberry/perl/lib). I guess CPAN will have problems if anything depends on I::M, but none of the modules I need do, so this works for me.

Those paths are from memory, so please message me if I ought to correct any of them.