Thanks, monk! You've been tremendously helpful! I now do something like:

use CAM::PDF;
use Encode "from_to";
my $pdf = CAM::PDF->new('myfile.pdf');

for ($pdf->getFormFieldList) {
    my $val = $pdf->getFormField($_)->{value}{value}{V}{value};
    if ($val =~ /^\x{fe}\x{ff}/) {from_to ($val,"UTF-16BE", "utf8")}
    print "$_ => $val\n";
}
[download]

and it works perfectly!