While Steve writes that he disagrees with the ego-transcending approach, he basically goes on and writes about transcending it, e.g. not "getting rid of it", but expanding our sense of self to embrace the whole of existence.
Although there are thousands of books written about how things look from such a perspective, it won't be possible for us to live and verify such a reality for ourselves, until a certain transformation occurs in us.
So to be able to see ourselves and one's own limited self as an expression of the one thing, and to live in such a condition, what do we have to do?
There are a lot of approaches, but the fastest and most effective way is
deep meditation.
If we only analyze our own actions, but at the same time are attached to who we think we are and what we do, it is not an effective approach.
It might be deceptively simple to rationaly see how we're not a limited self, how we're part of the organism, but again, to live this and to know this without additional rational mindframe is a truly different thing.
For such a change in perception to occur, we need to go deep into ourselves everyday, to touch the silent awareness that is beyond our mind and thoughts, and to gradually become capable of living from this place of inner stillness - with joy and love.
If we want to really transform ourselves, our perspective, we need to work on this everyday, consistently, regularly. That means we need a set of tools that are effective and that work. Well, I've already mentioned deep meditation and I cannot recommend it enough - give it a shot. It takes a few weeks, but rather days to see the results.
Take care and be smart - meditate