If you read old Universalist polemic (or old Unitarian polemic for that matter) you would be convinced that, on the face of it, we were arch biblicists. But I have a hard time reading our tradition(s) that way. I think the Universalists (in particular) were fond disputants, and the Bible was the acceptable vehicle of dispute. One gets a sense studying these forebears (and I hope I'm not projecting too much here) that the relationship with scripture is far more devotional and inspirational than dogmatic. For instance, the "Concordant Universalists" are more biblicist, and they cast a distinguishing light on "our brand" Universalists. These traits fit with the general pietistic thrust of American Protestantism.
But these traits are less helpful in finding or articulating a theology of revelation. Can't describe revelation, and you can't describe the transmission of tradition. Can't do that and there's little hope of starting self-consciously self-integrated churches. All you have left is custom and sectarianism, and that's what the UUA is chugging along on, ecclesiologically. Much of the mainline is little better shape.
So quite properly, unless you know who are, and how you got here, there isn't much hope in welcoming and including others. As Christians, we need to come to terms with (note, I didn't write "adopt wholesale") revelation, scripture, the universal Church, sacraments (perhaps worship generally) and the creeds. Much of what has been considered (and derided) as optional really stands as foundational. These are the main means of transmitting the tradition, and unless we know where we stand, we're adrift.