YHVH is not an egregore.
YHVH is a deity, not an egregore.
Make this distinction first. First, they’re different, second, it’s not respectful to those who practice within the Abrahamic paradigm to call the Godhead an egregore.
What you’re really asking is not to work within an Abrahamic paradigm, or not being chained down to an Abrahamic paradigm—which is fine. This is a common request and many people feel the way you do.
As to the other parts of your question—the LBRP, while originating as something linked to the Judeo-Christian elements of the Western Mystery Tradition, is something that is a highly flexible ritual. This is why it is known as “the neophyte meditation”; it’s made to be experimented with. I am sure you could find a version of this banishing ritual that is not exclusively linked to the Abrahamic paradigm. Wiccans, Hellenic polytheists, Khemeticists, and others have all adapted this ritual for use within their own belief systems. Do some searching around. My suggestion to you would to be to have a system in mind that will be the primary foundation of your Great Work before you go looking for the LBRP that will suit your needs. I am a Hermeticist, so I work within that frame. I use a Golden Dawn style banishing ritual.
Banishing, by its very nature, does not “attract” energy. Its very purpose is to banish or make things go away. Banishing dispels energy and entities. Invocation and evocation, however, do attract entities. The LIRP is different from the LBRP, and although the rituals are quite similar their functions are very different. Technically a magician should perform an LIRP in the morning and an LBRP in the evening, and for a while I tried to get into this routine, except that I was forgetting to banish in the evening.
The result? I ended up attaching myself with energies as each day passed where I did an invocation and not a banishing. Things got clunky, I felt “heavy” and especially empathetic/attractive to astral beings. My dreams turned especially vivid/nasty for a time. I suffered headaches, and minor misfortunes throughout the day. If you cannot maintain a schedule that fits in two daily rituals, please, please, only banish. Invoking without banishing will basically allow the floodgates to open to your personal astral bubble without closing them.
You have no fear of attracting energies by starting with a banishing ritual. That is another reason it is given to neophytes. For protection.
My experience with the LBRP have been very positive. It has done what it has needed to do to serve my neophyte needs: as a meditation, a way to communicate with my HGA, a way to strengthen my visualization, feel the Divine Presence, expand and sharpen my astral senses, enforce and reify my belief in the power of magick, and experiment with ways of entering and maintaining gnosis. These skills are ones you will carry with you into The Middle Pillar Ritual and others afterwards. The LBRP is a magickal life skill similar to knowing CPR or First Aid. It is indispensable safety and skill knowledge. Crowley wrote that those who do not appreciate or disregard the power of the banishing ritual, “are not fit to possess it.” I wholeheartedly agree.
I do not know very much about the Eastern Tradition but I will tell you that attempting to work with both the Western and Eastern System together will result in a) a lot of confusion to the beginner on which system is appropriate to use when and where and b) systems that actively oppose each other or two metaphysical systems that actively contradict one another will work to nullify or reject the other. Magick, like water, flows through the easiest path. Working with an Eastern system and a Western system together at the very least will cancel each other out, at the very worst will both be unfamiliar and hard to learn—and that is a sure recipe for your magick to fail. Commit to one for now. Later, as a more experienced magus, you can delve into the other tradition.
I love the Western Mystery Tradition and it makes me happy and proud of both my Catholic and Jewish roots.
Psst. Psst. Hey kid. Yeah you. Over here, around the corner. I got some chaos magick for you.