I found out why it wasn't working. I used identical meta_keys to ones already used in the fixed form elements. I'm hugely embarrassed, but now the code works fine. I'm sorry to have wasted so much of your and other's time.
In Registration Form with ID = 199 using the Edit Profile: [wpuf_profile type="profile" id="199"] I have following fields:
As you can see the meta_keys are now edu_programme2 respectively edu_institute2, but they originally were edu_programme and edu_institute. However, the fields added by the action hookeducation-hook still don't save their values. In the code I used the following code: