I fixed this by removing the preceding forward slash on Line 11 in default.pdt from this:
array('name'=>$this->_("HtmlInvoice.pay_invoice", true), 'attributes'=>array("href"=>$this->Html->safe($this->client_uri . "/pay/method/". $invoice->id ."/"))),
to this:
array('name'=>$this->_("HtmlInvoice.pay_invoice", true), 'attributes'=>array("href"=>$this->Html->safe($this->client_uri . "pay/method/". $invoice->id ."/"))),
Make Payment URL works fine now.