Advaita Vedanta is the tradition of non-dual metaphysics and the means of its realization as it has been transmitted in India. Its central teaching is the identity, complementarity, and harmony of the objective (transcendent) and subjective (immanent) qualities of the Absolute.
As you so aptly pointed out, the exoteric framework of this esoteric path is the revealed form of worship and civilization which has come to be known as Hinduism and which possesses certain inherent restrictions concerning its accessibility to those who are mentally and geographically foreign to it. As a darshan, that is, when viewed within the context of the Vedic tradition, it is heterodox to attempt the practice of Advaita Vedanta independent of its religious foundation irrespective of the withdrawal away from the proliferation of exterior forms of worship that takes place as a matter of course.
However, and here is where your question can potentially take on new meaning, metaphysics is the knowledge of reality. As such, it is one and universal however diverse are the forms wherein its exposition is clothed or however diverse are the forms of the souls wherein its realization takes place. One of the chief gifts of Frithjof Schuon is the manner in which he has exposed and formulated anew the universal meaning of the Vedantic doctrine and method, identified its analogues within other traditions, and assisted in the revitalization and preservation of esoterism in diverse religious contexts.
The three principle sadhanas of Advaita Vedanta are sravana (hearing), manana (reflection), and nididhyasana (meditation). Sravana is the formal Initiatic transmission of the scriptures in originally established by the primordial rishis who heard them within the depths of the heart, hence their designation as sruti or 'that which is heard.' Manana is the contemplation of the metaphysical doctrine contained in the scriptures and nididhyasana is the methodical concentration upon and total absorption within Brahman which may involve the use of a revealed mantra (literally manana trayate, that which when repeated saves).
According to Schuon, these sadhanas when considered in their universal content and significance as initiatic transmission (orthodoxy), metaphysical contemplation (doctrine), and methodical concentration (method), constitute the framework of all forms of esoterism. They may be found accessible in all authentic traditions wherever esoterism still thrives. It is in the context of this understanding that the notion of spiritual expediency arises within the teachings of the traditional school revealing a means by which Advaita Vedanta may in principle if not in fact be practiced outside of the Hindu context.