Why are export field mappings not available for custom search results?
Martin - one of our team had a quick dig. He says there is code that is intentionally preventing this, presumably as there is no presumption on what entity (member/contact/activity) is involved in the search.

Code involved is here: https://github.com/civicrm/civicrm-core/blob/master/CRM/Export/Form/Select.php#L81-L88

If that is enough for you to make a custom change (hack) to your system to get you over the hurdle, then good luck (normal warnings apply ie backup, etc)

If you would like us to work with you to sort this out either just for your situation, or a more generic fix that could end up as a community contribution (change to core, extension etc) then pls get in touch.