I compiled this into an actual shared circle.

https://plus.google.com/116347431032639424492/posts/BGk6DaqU...

I scraped the site with

  [].slice.call(document.querySelectorAll('a[href^="/track"]'),0).map(function(e){return e.href.replace(/.*\//g,'')}) 

and then I use

  var src = ["104448221006262595331", "102308414709447205951",...]; /*insert urls from above here*/
  var blah = src.map(function(e){return [["",null,e],"",[]]});
  var x = new XMLHttpRequest();x.open('post','https://plus.google.com/_/socialgraph/mutate/modifymemberships/?_reqid=333888252&rt=j,true);x.setRequestHeader('content-type',"application/x-www-form-urlencoded");x.send('m=['+JSON.stringify(blah)+']&a=[[["REDACTED"]]]&r=[[]]&at=REDACTED&')

To update the circle.

Edit: Updated the script to reflect site changes

Edit: It looks like sharing a circle doesn't include future changes.

Edit: you can skip the first step and instead use http://hngp.axxim.net/home/json