There are also other means to achieve the goal. According to Yalgniki upanishad, there are 12 means. Given these many means/methods to achieve the goal, which specific means is the author referring to here?
The author belongs to the Srivaishnava sect, a follower of Swami Ramanuja, and the Aazhwaar saints of South India. The method he is referring to is the same method adopted by Swami Ramanuja, his predecessors and his followers - called "Nyasam" or "Sharanagati. (Surrender)"
In order to establish the connection between Purushakaaram and Upaayam stated in shloka 6, we need to understand "surrender" a little better. Who do you surrender to? Of course the Lord. So the real means to achieving the goal is not the "act of surrender" but the Lord Himself. This brings us to an interesting situation. The Lord sees each of us not as the beings that we presently are (in this human body), but as the Indweller with the Baggage of Karma lasting billions and trillions of years (actually it has no beginning...). The moment he sees the Indweller he cannot but feel angry towards all the sins committed by the Indweller in all the past lifes (which we in this human body are not aware of). He is determined not to grant Moksha to this Indweller. So the Upaayam is actually insufficient to achieve the goal. Then why call it a "means to achieving the goal?" Because it is the last thing an Indweller can do to achieve its goal. However, the means works through a supporting means - called Purushakaram. His Divine Consort, the Lady intervenes at that point and recommends Him to accept the Indweller despite all its sins and short-comings. This she does out of the compassion she has for the Indweller that has come to surrender at His Feet.
But Wait ...did we not say earlier that Moksha is realized when we have rid the Baggage off its good and bad karmas. Why should the Lord get angry now? Because, "Surrender" is the only means through which an Indweller can achieve Moksham even when the Baggage is still full.! On the other hand, means such as Karma, Gnyana, and Bhakti lead to Moksha when the Baggage is empty - and therefore could take another millions of years. It is only in "Surrender" that the Lord has assured (As Devaperumal of Kanchi to Thirukkachi Nambi) that an Indweller can achieve "Dehaavastaane Moksham" i.e Moksham when the "present body falls". Call it if you will - the short-cut to Moksham. Because that is what it really is. While there are still those great stalwarts of Karma, Gnyana, Bhakti Yogas - including the demi-gods and rishis, and saints of yester-yugas still waiting in queue for their time to reach Moksham, the Lord has assured that the ones that "Surrender" will be given Moksham in short-cut at the end of the present life.! However, for this "Surrender" to work two things are important - 1. The act of surrender itself. 2. The recommendation of His Lady. The two work together to assure the Indweller of Moksham in short-cut at the end of this Life, no matter what the Baggage of Karma still holds.
That is why the author has together stated Upaayam (the means) and Purushakaaram (the recommendation) in Shloka 6.