That worked pretty well. Because I have another procedure to deal with things like PL/SQL procedures and functions, I had to rework it a little, so here's what I came up with. Another function calls this bit of code.

    my ($buffer, $line) = (undef, undef);
    my $read = true;
    while ($read)
    {
       $buffer = $curline->getline();
       if ( $buffer =~ m{;|/} ) 
       {
          $read = undef;
       }
       $line .= $buffer;
    }
        process_SQL($line);
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That won't handle the case where the lines are stacked up right on top of each other, but I think it'll work for the cases where we need it to.