I figured out that I needed the entries in the first ("root") array to be hash references. Below is the code used to generate this array.

    while($db->FetchRow()){                
        my %hash = $db->DataHash(@$fields_ref);
        push (@data, \%hash);
    }
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Whereas it was before

    while($db->FetchRow()){                
        push (@data, $db->DataHash(@$fields_ref));
    }
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The DataHash function returns a hash whose keys are field names (from the database) and whose values are the values of those fields on a specific row. I don't like defining %hash every time a new row is processed, but couldn't get any "one-liner" way of making it work. How might I go about writing the push line with $db->DataHash(@$fields_ref) treated as a hash reference. In case anyone's interested, I touched up the code I originally posted. There were a few minor mistakes which caused some confusion about my looping.

    while ($data[$x]){
        my ($i,@orderdata,%myhash);
        foreach $i (1 .. $numpix){
            if ($i == $data[$x]{'picorder'}){
$myhash{'orderline'} = "<option value=\"$i\" selected>$i</option>";
                }else{
$myhash{'orderline'} = "<option value=\"$i\" selected>$i</option>";}
            push (@orderdata, \%myhash);    
        }
        $data[$x]{'orderdata'} = \@orderdata;
        #transform anaglyph data for checkboxes
        if ($data[$x]{'anaglyph'} eq "Yes"){
$data[$x]{'anaglyph'}="checked";}
        $x++;
    }
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Everything seems to work. Thanks for your help