You're right, this ends up going down a different path. If you are able to insert the data into the database, all you'll need to change is the function on line 148 of lib/User.class.php to this:
function get_user_data() {
return array (
'memberid' => $this->userid,
'email' => $this->email,
'fname' => $this->fname,
'lname' => $this->lname,
'phone' => $this->phone,
'institution'=> $this->inst,
'position' => $this->position,
'perms' => $this->perms,
'logon_name'=> $this->logon_name,
'new_field_name' => $this->new_field_value
);
}
And change the load_by_id() function on line 57 to set the class variable (you'll need to declare it up at the top just like the rest of them). So..
$this->new_field_value = $u['new_field_name'];