If I correctly understand your question then you can add one more method, for example, with the name filterUsersOnGroup, which parameter is the sys_id of the group, chosen in assignment_group. The Reference qual of "Assigned to" field could be:

javascript:new BackfillAssignmentGroup().filterUsersOnGroup(current.assignment_group)

The code of filterUsersOnGroup could be the following

var BackfillAssignmentGroup = Class.create();
BackfillAssignmentGroup.prototype = {
    initialize: function() {
    },
    // Filter out groups that are not the provided type
    filterGroupsonUser: function(cUser) {
        ... // your old code
    },
    filterUsersOnGroup: function(group) {
        if (!group) {
            return;
        }

        var gr = new GlideRecord('sys_user_grmember');
        gr.addQuery('group', group);
        gr.query();

        var users = [];
        while (gr.next()) {
            users.push(gr.user);
        }

        return users.length > 0 ? 'sys_idIN' + users.join() : undefined;
    },
    type: 'BackfillAssignmentGroup'
}