As Anglicans, that we already are neo monastic, but many of us don't know it. Our ethos is Benedictine at the core as a tribe, based in ora and labora (prayer and work) or as I like to translate it (liturgy and mission). Attending to our spiritual life, weekly eucharist, daily office prayers, discernment... all these things are 'monastic.' Anglicanism is kind of like a monastic order for all. The Rule is the Baptismal Covenant.
So Chris, I'd say just begin to give attention and intentionality to our tradition to find the inner monastic. Also there are a few Anglican emerging churches that view themselves as such (are aware of it being latent in our tradition already) and are just keen to give it focus and more intentionality.
Also check out this NING site: http://new-monasticism-network.ning.com/
I also suggest this book: http://www.cms-uk.org/Community/Smallmissionalcommunities/tabid/442...
I'm looking at the Forward Movement 'Hour By Hour', here on the internet, and it looks like its the same as what's included in the Book of Common Prayer. Does it include the Daily Office Lectionary so you can keep up with the readings? It's a super handy way to keep steady pace through the Bible. With one little tweak, you can do the whole Bible in a year.
'Cave, Refectory Road' is the book by Ian Adams. It is on Amazon for purchase.
Sounds like you've already found some good responses, Christopher. Karen's sense of "latent monasticsm for all" is definitely something that drew me to the Anglican tradition too (my recieving church, the Crossing in Boston was planted by her neo-monstic/emerging community in Seattle and we remain sister churches). There is alot of talk about this movement now, but I personally see it grounded in many other periods of history--from some of the radical desert communities that sprang up around the time of Constantine as the FIRST monastics, to creative communities in Europe during the Reformation (Diane Butler Bass' "The People's History of Christianity" has some great gems across church history), to Dorothy Day's Catholic Worker movement. Wherever a point in history has spoken to hearts as crying out for the Gospel, people of have found ways to live it out radically in many ways, single or married, etc.
Personally, the best advice I think I can give is to pray and seek out others to support you in your practice- I've found an intentional praying community can be so helpful. It need not mean you have a monastery next door, maybe you simply find a small group or "soul friend" to pray the office or some other practice regularly. My church in Boston started the practice of having people commit to keep vigil a half hour or so before Mass, praying for the needs of the community and world, open to anyone who wanted to drop in. There were 3-4 core members who "held the space," but it was open to all, and having them there was deeply moving. Some of these same people have been exploring actually starting a "church house" together across town, living together in community in connection to our church's life of prayer and existing community outreaches. Claybourne and many of the other early "neo-monastics" seem to have worked similarly- just discerning where God might be leading new forms of community. For me, its meant getting together with some alumni of the intentional community I lived in last year to continue to live nearby or pray together at various points. Even a few times a week can be so powerful.
The daily office is a powerful spiritual practice, and a good one. If you're looking for some more resources, this is the first in a series of "ancient practices" that came out a few years ago, with an aim to making monastic ways accessible to people right where they are. Folks from diverse backgrounds, though alot of emergent, Anglican or "closet Anglican" (McLaren has been coming out alot on recent years) folks in there: http://www.amazon.com/Finding-Our-Way-Again-Practices/dp/0849901146
Shane Clayborne has been mentioned- you might appreciate this office book, co-authored by several leading figures in the "neo-monastic" world with a deep heart for social justice and living one's prayers in relation to various saints and martyrs for the oppressed down through history. Its very heartfelt and accessible, influenced by the Anglican and other prayer resources.
As far as recognition goes, there are many Anglican orders out there that have "wider orders" or "lay fellowships" for people feeling a connection but who can't commit to celibacy or a cloistered life. I have many friends of the Order of St. John the Evangelist in Cambridge, MA. The Order of Julian of Norwich is another. Many of these have annual gatherings at a "Motherhouse" and seek ways to connect across long distances. My friend who joined the Order of Julian took lay-vows to the rule during the worship of our Episcopal community in Omaha, even though we were not members she asked us to witness and support her in her vocation.
As far as new movements go, there are many springing up across denominations-- Claybourne's is the "Simple Way" in Philidelphia, deeply engaged in radical hospitality and the rights of the poor and homeless of their city. "Rutba House" was started by one of his friends, a gentleman injured in Iraq while serving as a Christian Peacemaker human rights witness and touched by the hospitality of Iraqi's who cared for him. His story is in this book on neo-monasticism:
He also helped gather folks from around the country to explore common "marks for mission" alot of these seem to share: