Programmatically submit form / save all nodes
I don't think trying to fake form submissions is a good idea - there is a lot that goes on behind the scenes, and it is easy to get something wrong.

I would suggest instead you implement a script similar to the one you pointed out in Load and Save nodes with script? in which you actually set the missing values to the empty data you require. In that script, after the node_load (and before the node_save) you could do something like:

$empty_value = array(
  'value' =&gt; ''
);
$node-&gt;field_my_custom_field[$node-&gt;language] = array(
  0 =&gt; $empty_value
);


You would need to do this for each field that needs fixing. The value you need for $empty_value will depend on the field type. You could work it out dynamically by calling field_info_field ;  however as your script is a one-off, it's simpler to just set the right value for each field. To know what the right empty value should be, just create a node with the right empty value and then inspect it (eg. using var_dump, dpm, etc.)