Bam! Got it. I set the "density" setting to "300x300" when reading the image in, by default it is set to 72 dpi.

PDF::OCR2 is now reading the text in the cropped rectangle flawlessly.

Thanks for pointing me in the right direction.

Here is the sample code:

use Image::Magick;
use PDF::OCR2;

my $image = Image::Magick->new;
$image->Set(density=>'300x300');
$image->Read('agendas/2016-02-02 Natural Resources.pdf', compression=>
+'None');
$image->Crop(geometry=>'1248x520+936+520');
$image->Write(filename=>'crop.pdf', compression=>'None');

my $p      = PDF::OCR2->new('crop.pdf');
my $text_all = $p->text;

print $text_all;
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