There are actually a number of "Independent Catholic Churches". There was one at one time called the
Independent Catholic Churches International that sought to bring them together. Their Bishop Fred Jones was invovled in a number of Progressive Christian projects (media related with people like Spong Reuther and so on). He was dually affiliated with the UCC.
There is the Apostolic Catholic Church that has a number of parishes
http://www.apostoliccatholicchurch.com/They note:
"The Apostolic Catholic Church is one of the larger old catholic groups in North American. In contrast to most old catholic/ independent catholic groups the Apostolic Catholic Church has more active communities than it has clergy". They are progressive and diverse.
The Apostolic Catholic Church is a member of the
International Council of Community Churches (who along with the Episcopal Church, Presbyterian USA, United Church of Christ and about five or six other make up Churches Uniting in Christ who are working for intercommunion and mutual recognition of ministries).
http://www.icccusa.com/ICCC is itself a mainline and diverse denomination (if you will pardon the term). They are made up of many independent churches, ministries and missions. Some more conservative than others. ICCC is a member of the National Council of Churches and World Council of Churches.
{Note: I am not connected to the Apostolic Catholic Church. Thought I would make it plain so it does not look like self promotion for them. I am in a ministry connected to ICCC}. I will see if I can find some other links for you.