Restrict choice of menus available on basis of assigned domain

Background
Thanks for this wonderful module. I should say that this issue has evolved from a previous entry. The title of the original post doesn't correspond with my current issue, so I'm creating a new one here.
(if you're interested, I'm referring to this issue).

Issue
I wonder if anyone knows of a way to 'restrict' the choice of menus available when an administrator of a sub-domain (i.e. a Domain Access module 'domain') creates content, such as a new basic page, and wants to add that page to the menu (using the Menu settings > Provide a menu link option) so that he or she can only add the new page to their assigned domain? If this makes sense...

Steps tried so far
I've tried altering the menu settings on each domain (I have approx 100 domains), to 'set a source for the main links' but this has no effect. I wonder what I'm missing? My problem is that with around 100 domains worldwide and over 100 administrators each managing their own domain, it is currently too easy to accidentally add a new piece of content to the wrong menu (using the Menu settings > Provide a menu link option). It would be great if there was option to set the default selected menu to e.g. the user's assigned domain. Perhaps this functionality already exists and I'm just not seeing it.

A suggestion and possible solution, but don't know how to apply it
@agentrickard has suggested a using a form_alter. I'm afraid this is beyond my coding skills at the moment. However, I did find the code below on stackoverflow (which I haven't tried yet). I wonder if this is this the kind of thing you were suggesting when referring to a 'form_alter'?
Can it be added as it is below or do I need to make any edits, to e.g. 'MYMODULE' (as I said, coding is not my thing - yet! Willing to learn but currently afraid of somehow corrupting my site or db):

function MYMODULE_form_page_node_form_alter(&$form, &$form_state) {
  global $_domain;
  if (isset($_domain['domain_id'])) { // only display domain's primary links
    $menus[domain_conf_variable_get($_domain['domain_id'], 'menu_main_links_source')] = $_domain['sitename'].' Main menu';
  }
  if (isset($menus)) {
    $options = menu_parent_options($menus, $form['#node']->type);
    $form['menu']['link']['parent']['#options'] = $options;
  }
}

thanks again,
A~