First off all I want to say I recognize your feeling. Luckily, many Buddhist centers and monasteries that can take you up from anywhere ranging from a day till possibly your entire life. There are many in the US, also. If you are in a point of your life where you are able to visit one for a considerable time, I would really encourage you to do so. Don't rush it, however. For example, I wouldn't start by planning to go somewhere forever. People who rush in with those sorts of ideas often quickly run back home again.
So my advice is to perhaps find a local group, get some connections. Then plan a retreat or some, like a week or so. Just to see if this is really what you want and to get familiar with it. Via via you will find some places and monasteries and you will also learn what fits you best.
The bartering thing isn't really needed. People like it if you have something to offer, but in my experience they don't ask for such a 'contract'. Instead just ask places if there is a possibility for a visit and for how long. Sometimes they will ask for money to fund the retreats and whatnot, sometimes not. Most important thing is you find a place where you find yourself fitting in.
Myself I've been visiting groups and monasteries for years and soon I am going off with the intention to ordain as a monk. Not in the US though, I'm from Europe so I can't really help location wise.
Edit: I saw the article wrote an entire how-to guide and stuff. A bit over the top if you ask me. And certainly the thing about a non-buddhist having to offer more to come into a Buddhist monastery is silly.
There is no definition of a Buddhist anyway.
But how it went for me for a long retreat: I contacted a monastery I went on a retreat before. Asked via email if I could stay as I knew they needed some general help in the winter retreat time. They allowed me to come over even though they already found other people to help out. That was it, really. They knew me already, so that helped.
Another place I sent an email to stay for a longer time. They said it was full. But some time later I got an email saying I was able to come by because somebody dropped out. (By that time I had planned other things though)
Sorter retreats usually aren't that big of a problem because many places organize them themselves and you can just subscribe.
Wish you the best!